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AN OUTLINE 



LAWS OF THOUGHT. 



AN OUTLINE 



OF THE NECESSARY 



LA¥S OF THOUGHT 



A TREATISE ON 



PURE AND APPLIED LOGIC. 



WILLIAM THOMSON, D.D., 

PB0V08T OP THE QUEEN'S COLLEGE, OXPOBD. 



FOURTH EDITION. 



NEW YORK: 
SHELDON AND COMPANY 

BOSTON: GOULD & LINCOLN. 

18 6 3. 






in Exchange 
Brown University 

JUL f 7 1934 






en 



TO 

SIR WILLIAM HAMILTON, Bart. 

PKOFESSOR OF IXJGIC AND METAPHYSICS IN THE 

UNIVERSITY OF EDINBURGH, 

ETC. ETC. 

THIS ESSAY 
IS, BY HIS PERMISSION, INSCRIBED. 



TLaTifj (/£v ovv Kol -^eia, ev l(r9t, v bofifi, riv bpfig^ Inl rovg 2j6yovQ- IXkvoov 
6e aavrbv Kal yviwaaai iiuXaov 6ta TTJg Soiiovaijc uxpfiarov sivac /cat KaTixwfii' 
VTjQ vnh Tuv TTO/lAwv wSo^eaxia?, S<'K £" vso^ el • fi de urj, ae duKpev^ercu i] 
u^ai&eui. 

Plato. 



PREFACE. 




OME account of the exact position which 
this work pretends to occupy amidst a 
crowd of valuable treatises on the same 
subject, may not be an unfitting intro- 
duction to its pages. The system of Pure Logic or 
Analytic that has been universally accepted for cen- 
turies past, is very defective as an instrument for the 
analysis of natural reasoning. Arguments that com- 
mend themselves to any untaught mind as valid and 
practically important, have no place in a system that 
professedly includes all reasoning w^hatever ; and an 
attempt to reduce to its technical forms the first few 
pages of any scientific work, has generally ended in 
failure and disgust. The consequence has been that 
the more popular writers on Logic have begun to 
treat its strictly technical parts with a certain coy- 
ness and reserve. They have denied to the rules of 
the syllogism that prominent place once assigned to 
them, yet at the same time they have refrained from 
lejecting as cumbrous and unnecessary an instrument 



viu PEEFACE. 

which did not subserve any practical end in their 
systems. 

The present work is an attempt to enlarge the sci- 
ence of Pure Logic, so that it may be adequate to 
the analysis of any act of reasoning. How far it 
has attained its object ought to be decided by the ap- 
plication of its principles to many miscellaneous ex- 
amples from different sciences ; and whilst I have 
rigorously and frequently applied this test to it for 
many years, I cannot hope that the partiality of an 
author will be a suiBcient guarantee of its preten- 
sions, and therefore commend the same line of exam- 
ination to any one who believes, with me, that a sed- 
ulous practice of logical analysis will richly reward 
the understanding with accessions of strength and 
clearsightedness. If the result should be the detec- 
tion of many errors and omissions on the author's 
part, enough of matter may perhaps be left unshaken, 
to prove that Pure Logic is not the mere ojfficina ve- 
teramentaria — the warehouse of useless relics — it is 
too often taken for, but a practical system — an im- 
portant branch of mental culture. 

To Sir William Hamilton, of Edinburgh, whose 
death every student of philosophy may deplore as a 
personal loss, I am greatly indebted for valuable as- 
sistance, freely and generously afforded, at the cost 
of much time and trouble. There is no longer any 
feax that such an acknowledgment will be miscon- 
strued into an admission that the present work only 



PREFACE. IX 

reports the opinions of that illustrious philosopher ; 
as he has himself recognized its claim to an indepen- 
dent position.* In truth, the extension of the syllo- 
gism, the enlarged list of immediate inferences, the 
doctrine of the three aspects of propositions, in 
Extension, Intension, and Denomination, and the 
grounds for rejecting the Fourth Figure of Syllogism, 
which serve, with other things, to give this little book 
its character, were worked out originally without as- 
sistance from any living author, from such materials 
as any student might command ; and it may perhaps 
be permitted me, without seeming to court a damag- 
ing comparison, to point out that the twelve affirma- 
tive modes of Syllogism in each figure, which here 
replace the much more limited number of the old 
system, are precisely those which Sir William Ham- 
ilton has found it necessary, on his own principles, to 
adopt. This will be an evidence to the reader that 
the alteration in question is not rash and arbitrary. 

To Professor De Morgan, who has put forth, be- 
sides many excellent Mathematical Books and Es- 
says, an elaborate and acute Treatise on Formal 
Logic, my best acknowledgments are due for his kind 
and patient explanations of certain parts of his sys- 
tem. Other obligations to him are notified in their 
proper places. 

The Appendix on Indian Logic, by my friend Pro- 
fessor Max Miiller, of Oxford, whose philological prO' 

* Sir W. Hamilton's Discussions in Philosophy, p. 126. 



X PREFACE. 

ductions have already made his name known ovei 
three continents, although they are but the first gath- 
erings of a harvest rich in promise, is intended to call 
attention to the interesting resemblances between the 
Greek and Hindu systems, which have never yet re- 
ceived the consideration they deserve. 

The favour with which this book has been received, 
has far exceeded the expectations of its writer. It is 
now adopted as a class-book in several places of 
education; and the careful revision of the present 
edition may perhaps have rendered it more fit for 
such a use. 

W. T. 
Qaeen' 3 College Oxford : Jane, 1867. 



TABLE OF CONTENTS. 



Inteoduction. 

IICT. PAO> 

1. Processes precede laws 17 

2. Origin of Logic 18 

8. Logic, pure and applied 20 

4. Tliis distinction defended 21 

5. Pure Logic 23 

6. Logic a Science 26 

7. Unconsciousness in Art 28 

8. Logic a practical Science 30 

9. Logic defined 30 

10. Its limits 32 

11^15. Form and Matter 33 

16. Pirst and Second Intentions 40 

Language. 

17. Thought and Language 42 

18. Language defined 43 

19. Language has fotir functions 43 

20. It aids analysis 44 

21. Degrees of this power 45 

22. Speech the highest language. Why 1 48 

23. 24. It records thoughts 49 

25. It shortens thinking 52 

26. It communicates thoughts 54 

26*. Aristotle's view of words 56 

27. Speech not essential to thought 58 

28. Though signs may be 60 

29. Origin of language 61 

30. 31. Growth of language 63 



xii CONTENTS. 

BECT. PA«I 

Introduction Concluded. 

32-34. Logic is d priori 66 

35. Twelve names of Logic 71 

36. Uses and pretensions of Logic 74 

37. Its practical value 78 

38. Neglect of its details 80 

39. Which are shortened, not simplified 82 

40. Division of Logic 83 

41-43. Objections 84 

44. Method.. , 86 

45. Use of Logic 86 

Part I. Conceptions. 

46. Cognitions in general 91 

47. Intuitions and Conceptions 93 

48. Formation of Conceptions 94 

49. Higher and Lower Conceptions 96 

50. Genus, Species, Individual 97 

51. Marks or Attributes 98 

62. Extension and Intension 99 

63. Determination 102 

64. Three powers of Conception 102 

55. Logical Division 103 

56. Partition 107 

67. Definition 107 

{^S. Denomination 110 

59. Privative Conceptions 112 

60. Kelative Conceptions 114 

61. Abstract and Concrete Representations 116 

62. Nature of General Notions 116 

65. Questions about Conceptions 124 

<^. Summary 127 

Part II. Judgment. 

67. Judgment defined 133 

68. Doctrine of Relation in Judgments 134 

69. The two Predicable-Classes 136 

70. Definition explained 142 

^ 71. Sources of Definition 143 

L^ Table of Definition 145 

72. Attribute 145 

73. Common View of Relation 145 



CONTENTS. Xui 

■ECT. PAGB 

74. Doctrine of Quantity 163 

75. Doctrine of Quality 154 

.ir_76. Doctrine of Modality 155 

. 77. Distribution of Terms in Judgments 156 

78. Table of all the Judgments i 160 

79. The same, according to Sir W. Hamilton 162 

80. Import of Judgments. Extension and Intension. Naming. 165 

81. Explicative and Ampliative Judgments 168 

Part III. Syllogism. Eeasoning. 

82. SyUogism 173 

83. Immediate and Mediate Inference 174 

84. Opposition and its Inferences 177 

85. Conversion and its Inferences 182 

*^^6. Inference by Privative Conceptions 185 

87. Inference by Added Determinants 187 

88. Inference by Complex Conceptions 188 

89. Inference by Interpretation 188 

90. Inference by Disjunctive Judgments 190 

91. Inference by Sum of Predicates 191 

^ 9 2. Concluding Remark. 191 

93. Canon of Mediate Inference 192 

94. Order of Premisses 199 

95. The Three Figures , 201 

96. Special Canons of the Figures 205 

<97. The Fourth Figure 206 

98. The Unfigured Syllogism 208 

99. Modes of Syllogism 209 

100. Table of Modes 209 

101. A Mode of Notation 211 

102. Equivalent Syllogisms 215 

103. Sir W. Hamilton's Notation 218 

104. Euler's Notation 220 

105. Inference in Extension, Intension, and Denomination 222 

106. Conditional Syllogisms 224 

107. Disjunctive Syllogisms 230 

108. Complex Syllogisms. Sorites 233 

109. Dilemma 236 

110. Incomplete Syllogisms 239 

111. Prosyllogism and Episyllogism 240 



xiv CONTENTS. 

SECT. PAQB 

Part IV. Applied Logic. 

112. Province of Applied Logic 245 

113. Science 246 

114. Criterion of Truth 247 

113. Induction and Deduction 251 

114. Search for Causes. Inductive Methods 254 

115. Anticipation 266 

116. CoUigation. Definition 269 

117. Complete and Incomplete Induction 272 

118. Degrees of Belief ." , 278 

119. Syllogism, Deductive and Inductive 281 

120. Employment of Defective Syllogisms 283 

121. Syllogisms of Analogy 289 

122. Syllogisms of Chance 293 

123. Syllogisms of Classification 302 

124. Nomenclature 304 

125. Sources of Principles 306 

126. Errors and Fallacies 309 

127. Dealing with Errors 309 

128. Method. Definition and Division 310 

129. Subordinate Parts of a Science 312 

130. Categories 313 

131. Division of the Sciences 315 

132. Conclusion 320 

Appendix. On Indian Logic (by Professor Max Miillor) 325 



OUTLINE 



LAWS OF THOUGHT. 



INTRODUCTION. 



'ELttujiev ovv Scci ^oax^uv rig rj npo-^ecig koc rig 6 aaonhg iraarii rfti ata 

Alsxandee Aphkod. 



OUTLINE 



LAWS OF THOUGHT. 




mTRODUCTION. 

" Nullam dicere maximarum rerum artem esse, cum miiumarum 
sine arte nulla sit, hominum est parum considerate loquentium atque 
in maximis rebus errantium/' Ciceko. 

VEE-Y process has laws, known or un- 
known, according to which it must take 
place. A consciousness of them is so far 
from being necessary to the process, that 
we cannot discover what they are, except by analyz- 
ing the results it has left us. Poems must have been 
written before Horace could compose an " Art of 
Poetry," which required the analysis and judicious 
criticism of works already in existence. Men poured 
out burning speeches and kindled their own emotions 
in the hearer's breast, before an Art of Rhetoric could 
be constructed. They tilled the ground, crossed the 
river or the sea, healed their sicknesses with medici- 
nal plants, before agriculture, chemistry, navigation, 
and medicine, had become sciences. And wherever 
our knowledge of the laws of any process has become 



18 OUTLINE OF THE 

more complete and accurate ; as in astronomy, by 
the substitution of the Copernican for the Ptolemaic 
system ; in history, by a wiser estimate than our 
fathers had the means of forming, of civilization and 
its tendencies ; in chemistry, by such discoveries as 
the atomic theory and the wonders of electro-mag- 
netism ; our progress has been made, not by mere 
poring in the closet over the rules already known, to 
revise and correct them by their own light, but by 
coming back again and again to the process as it 
went on in nature, to apply our rules to facts, and 
see how far they contridlcted or fell short of explain- 
ing them. Astronomers turned to the stars, where 
the laws they sought for were day and night fulfill- 
ing themselves before their eyes ; historians collected 
facts from the record<3 of different countries, watched 
men of many races, of various climates, differently 
helped or hindered, for there, they knew, the true 
principles of history were to be read ; and chemists, 
in the laboratory, untwisted the very fibres of matter, 
and watched its every pulse and change, to come at 
the laws which underlaid them. " Even geometry," 
says the great chemist, Justus Liebig, " had its foun- 
dation laid in experiments and observations ; most 
of its theorems had been seen in practical examples, 
before the science was established by abstract rea- 
soning. Thus, that the square of the hypothenuse 
of a right-angled triangle is equal to the sum of the 
squares of the other two sides, was an experimental 
discovery, or why did the discoverer sacrifice a heca- 
tomb when he made out its proof ? " 

§ 2. The same applies to Logic, or the science oj 
the laws of thought. The process of thought, or that 



LAWS OF THOUGHT. 19 

active function of the mind by which impressions 
received from within or from without are described, 
classified, and compared, commenced long before the 
rules to which it adheres with unfailing strictness, 
had been drawn out. And though they do not de- 
vend on experience — i. e. their truth may be tried and 
made manifest without recurring to examples — still 
without experience, without the power of watching 
our own thoughts and those of others, there could 
never have been a science of Logic, which had its 
origin when some reflective mind, that had for years 
performed the various acts of thought spontaneously, 
began to lay down the laws on which they take place, 
or to give rules for repeating them at pleasure. The 
clearest reasoner cannot with propriety be called a 
logician, so long as he disputes spontaneously and 
without rule ; whilst the man with the humblest rea- 
soning powers may lay claim to the title, in so far as 
he reasons according to laws, ascertained by reflec- 
tion upon the process of thinking. If, for example, 
we call Zeno of Elea the inventor of Dialectic or 
Logic in Greece, it is not in virtue of his marvel- 
lous ingenuity in arguing against the possibility of 
motion, because this might have been the result of 
natural acuteness ; but because his arguments, all 
constructed upon one type, that of forcing his antag- 
onists into an absurd position by reasonings drawn 
from their own views, seem to indicate the possession 
of a logical rule, the same which now has the name 
of reductio ad absurdum. He had reflected upon 
those modes of argument which his position led him 
to adopt spontaneously, and had formed a general 
rule or plan which assisted him in forming like argu* 



20 OUTLINE OF THE 

ments in future. Logic then, like Philosophy, of 
which it is a part, arises from the reflection of the 
mind upon its own processes ; a logician is not one 
who thinks, but one who can declare how he thinks. 
This important distinction, which has been too often 
neglected^ must govern all researches into the history 
of the science. 

§ 3. Logic has been defined to be the science of the 
necessary laws of thovght. But this definition, the 
correctness of which shall presently be examined 
more particularly, requires a few words of general 
explanation. Our thoughts are formed indeed by 
laws ; and when we conceive, abstract, define, judge, 
and deduce, we put in practice so many ascertaina- 
ble principles. But does Logic simply explain these 
laws in themselves, or contemplate them in their uses, 
as assisting and regulating our efforts in seeking after 
knowledge ? This distinction is analogous to that 
which is drawn between Anatomy and Physiology, 
the former of which simply examines what are the 
parts of the human frame, and the latter, the Science 
of Life, dwells upon the uses and developments of 
the parts : the one declares that I have a brain, and 
the other determines that it is the principal seat of 
passion, sensation, and reason ; and that it is weak 
in childhood, strong and constant in mature life, and 
subject to a gradual decay in age. It is competent 
to us unquestionably to consider the principles of 
thought under this twofold aspect of their nature and 
their employment. Thus, if we take a judgment; 
say, " The happiness of the human family will in- 
crease in pioportion to the increase of mutual love," 
and consider it in it^ own nature, we shall decide 



LAWS OF THOUGHT. 21 

that it is a judgment correct in form, that certain 
other judgments may be gathered from it, that it has 
some qualities which may belong to a judgment, and 
wants others ; and so far we are only looking at the 
judgment in itself, by M^hat we know of the laws of 
judgment. But if we consider this example in con- 
nection with truth and knowledge, we are led to ex- 
amine fm'ther, whether it is false or true, whether in 
forming it we fulfilled those conditions, of observa- 
tion and reasoning, without which we have no right 
to expect a true result ; to what region of thought it 
belongs, and what is the method, be it testimony, 
deduction from principles, or observation of facts, by 
which judgments are to be obtained in that region. 
In the former case we only put in requisition what 
may be called pure Logic, which is defined to be the 
science of the necessary laws of thought in their own 
nature ; whilst the questions in the latter case belong 
to applied Logic, or the science of the necessary laps 
of thought as employed in attaining truth. 

§ 4. But is this distinction worth preserving in our 
exposition of the science ? Many logicians, believ- 
ing that they must undertake to teach men " the art 
of reasoning," do not attach aliy value to the laws 
of thinking, except in so far as the employment of 
them may help men to think, and so to enlarge their 
stock of truth ; that is, they do not regard pure Logic 
as a distinct branch of their subject. But there is 
one grand reason for the opposite course. Truth is 
a wide word, and denotes all that we can ever know 
of ourselves, the universe, and the Creator. The 
science which explains how the mind deals with 
truth, must be loose and indefinite, as its object-mat* 




22 OUTLINE OF THE 

ter is of infinite extent ; so that applied Logic can 
never attain perfect completeness and precision, be- 
cause it can never affirm that it has shown how the 
mind deals with every part of truth and knowledge. 
But the laws of thought themselves are few in num- 
ber, and lie, in examples of perpetual occurrence, 
under every thinking man's observation ; and there- 
fore it may be declared with tolerable correctness 
when a full and accurate view of pure Logic has 
been taken. To secure that which we have com- 
pletely mastered, it is desirable to keep it separate 
from that in which perfect completeness is hopeless ; 
and therefore we purpose to consider Logic under 
two distinct lights, first as a science of laws, and 
next as a science of laws applied to practice. 

But here a caution is necessary (which we shall 
have to repeat in connection with the tiipartite divis- 
ion of pure Logic itself), that as the distinction is in 
a measure arbitrary, for the laws of thought are 
always put in force with a view to the attainment or 
communication of knowledge, it will be impossible 
to maintain it with perfect consistency throughout 
our labours. Occasions constantly arise when the 
line of demarcation becomes blurred and confused ; 
when the bare laws of thought cannot be explained 
without the mention of that truth, in the search for 
which they are always employed : thus, in treating 
of Definition, which is one form of judgment, we 
imply the existence of a person /or whom it is neces- 
sary to define a given notion that he may possess the 
true meaning of it, and be able to identify the things 
for which it stands. All that can be expected from 
us is, that, even if we find it necessary to repeat the 



m 



LAWS OF THOUGHT. 23 

same truths in the two divisions, we do not desert 
our point of view, but explain the laws of thought, 
first mainly for themselves, and then mainly in rela- 
tion to truth, which is the object of all thought and 
inquiry. 

§ 5. Pure Logic (which is later in the order of 
discovery than applied, inasmuch as it is formed by 
abstracting from that more general science) takes no 
account of the modes in which we collect the mate- 
rials of thought, such as Perception, Belief, Memory, 
Suggestion, Association of Ideas ; although these are 
all in one sense laws of thought.* Presupposing the 
possession of the materials, it only refers them to their 
proper head or principle, as conceptions, as subjects 
or predicates, as judgments, or as arguments. It 
enounces the laws we must observe in thinking, but 
does not explain the subsidiary processes, some or all 
of which must take place to allow us to think. Met- 
aphysics is the science in which these find place ; 
but they also belong to applied Logic, because they 
are so many conditions under which the human mind 
acquires knowledge. Again, in pure Logic, the dif- 

* " Now Tiniversal Logic is either pure or applied Logic. In the 
first we make abstraction of all empirical conditions, under which 
our understanding is exercised ; for example, of the influence of the 
senses — the play of the imagination — the laws of memory — the power 
of habit, of inclination, &c. ; consequently also of the sources of pre 
judices, nay, in fact, in general, of all causes out of which certain 
cognitions arise to us or are pretended to do so, since they merely 
concern the understanding under' certain circumstances of its appli- 
cation, and in order to know them, experience is requisite." — Kant's 
Critique, p. 58, Englisli transl. 1st ed. The ground here taken is 
different from that in the text. I do not say they are contingent, for 
memory, for example, enters into every act of thought ; but, that 
they are subsidiary ; thought is not complete without them, but at 
the same time thought is never complete with them alone. 



24 OUTLINE OF THE 

ferent processes of the mind are regarded in their 
perfect and complete state ; whilst in applied, the im^ 
perfect faculties of man, the limited opportunities 
of observation, the necessity of deciding upon a 
question when the materials of a judgment are still 
insufficient, impose many limitations on the perfec- 
tion of our knowledge. Thus, whilst pure Logic 
only treats of arguments that are certain and irrefut- 
able, the most important duty of applied Logic is to 
determine under what conditions imperfect argu- 
ments, such as the Example, the Imperfect Induc- 
tion, the Deduction from a proposition that is not 
truly universal, and some of the Rhetorical Enthy- 
menes, can be fairly employed, and to show, that 
though these weaker forms are so many deviations 
from a perfect demonstrative argument, they are so 
far from superseding the perfect forms, that in reality 
each of them appeals to, and attests the cogency of, 
some perfect form, to which it strives, as it were, to 
conform itself. As we are anticipating, a very easy 
example must suffice to illustrate our meaning. 
Every one is perfectly certain of the truth of the 
proposition that men groio infirm and die ; of which 
we have been convinced partly by our own experience 
of men, and partly by the experience of others, de- 
livered to us from all quarters, in the sober pages of 
the moralist as well as in the reckless lyrics of the 
reveller. Nor does our conviction of this truth per- 
mit itself to be distm-bed by the consideration, which 
is likewise undeniable, that the whole aggregate of 
this experience does not in itself warrant any state- 
ment having all mankind for its subject : that even 
supposing the decadence and death of every man in 



LAWS OF THOUGHT. 25 

times past had been observed, which is utterly incon- 
ceivable, at any rate there are many now living upon 
whom the common doom has not passed, and whose 
cases therefore cannot enter into the sum of our ex- 
perience. In a word, we have concluded from an 
experience that inany men have become infirm and 
died, the much wider truth that all men do so ; and 
this is warrantable in the given case, and we are 
right in rejecting upon the faith of it an assertion, 
unless supported by evidence that transcends experi- 
ence, that one man has not died, such as we have in 
the fable of the Wandering Jew, or a proposal to 
obviate death in future, such as was involved in the 
search of the alchemist for an Elixir of Life. But 
that this mode of argument from a particular to a 
universal, from some to all,, is not valid in itself, is 
evident from applying it to another case, in which it 
is absurdly false — some meii are tall, therefore all men 
are tall : and the only form perfectly indisputable in 
itself would be, " the men whom we have observed 
have all died, and these men are all men, that is, the 
only men, therefore all men die," which from the 
nature of this case cannot be employed. But ap- 
plied Logic first shows that this perfect argument is 
the measure of the validity of the other ; that our 
conclusion is only true if we can say, not indeed 
"these men are ail men," which is impossible, but 
the equally general proposition, " These men are {as 
good as) all men ; " thus conforming really to the 
perfectly conclusive argument ; and next, how and 
under what circumstances we can cpnform the in- 
complete to the complete enumeration, how some 
can ever be said to be as good as all for purposes of 
argumentation . 



26 OUTLINE OF THE 

But it is time to proceed to examine the different 
parts of the definition of pure Logic, by showing 
that Logic is a science, rather than an art — that it 
is a science of the necessary laws or forms of 
thought — that it has thought rather than language 
for its adequate object-matter. 

§ 6. Logic is a science rather than an art. This 
distinction between science and art is, that a science 
is a body of principles and deductions, to explain 
some object-matter : an art is a body of precepts, 
with practical skill, for the completion of some w^ork. 
A science teaches us to know, and an art to do ; the 
former declares that something exists, with the laws 
and causes which belong to its existence, the latter 
teaches how something must be produced.* An art 
will of course admit into its limits every thing which 
can conduce to the performance of its proper work ; 
it can recognize no other principle of selection. The 
painter may fail of perfect success from employing 
improper colouring materials, or a muddy and perish- 
able varnish, as well as from incorrect drawing or 
ill-managed light and shade ; the lower defect or the 
higher is fatal to that perfect picture which he wishes 

^ Ilepl jevEGiv T£Xi^V, '^fp^ to ov hntaTiJiiTj. Aristotle, An. Post. ii. 
iix. 4. By Science in the text is meant the speculative science of 
Plato and Aristotle ; by Art the practical science. Plato seems to use 
TEXVTi and sTnGTrifiT] as interchangeable terms (Tkeat. 146, c). Again 
[Politicus, 258, d. e.) he divides EiTLaT?jfj.aL into irpaKTLKal and yvua- 
TUial; the latter he would subdivide (260, b.) into critical, which 
end in judging mef?fily, and epitactical, which lead us to some prac- 
tical result. See also Theoit. 202, d. Where Aristotle distinguishes 
between Science and Art, which is not invariably the case, he ex- 
plains them as A^e have done in the text, adding only that the object- 
matter of Science is necessary or invariable ; that of Art, contingent 
and variable. See An. Post. i. ii ; Top. vi. viii. 1 ; Eth. Nic. vi. ii; 



LAWS OF THOUGHT. 27 

to produce. So that an art may contain precepts 
of a very dissimilar character; the painter must be 
taught Expression, Anatomy, and mixing of Colours ; 
the Rhetorician must learn to manage his thoughts, 
his hearers, and his hands, with equal dexterity. 
The science, on the other hand, having the object- 
matter for its touchstone, admits nothing except 
what relates directly to it ; and so a far greatei 
unity and simplicity naturally belongs to it. Geome- 
try treats of nothing but the properties of space, 
because it is a pure science ; whilst the arts founded 
upon it, such as Land-surveying, must bring in such 
topics as inequalities of surface, use of instruments, 
and the like. The science of Musical Counterpoint 
teaches the theory of harmonic progressions, and 
nothing else ; but the musician's art, in which it is 
employed, must add the knowledge of instruments 
and their compass, of the human voice, even some- 
times of the powers of a particular singer. Now in 
the popular meaning of the word Logic, no doubt 
the notion of an art is more prominent ; to be able to 
reason better, and to expose errors in the reasoning 
of others, is supposed to be the object of this study.* 
But those writers who have followed out this view 
have been compelled to go over too wide a field for 
any one system. Logic must be the widest of all 
arts or sciences ; because thinking, which is its ob- 
ject-matter, belongs to all the rest ; it is ars artium, 
the art which comprehends all others, because its 
rules apply to every subject on which the human 

* Upon the historical view of the question, whether Logic is an 
Ajt or a Science, most valuable remarks will be found in a paper by 
Sir William Hamilton. Edinburgh Review, 115, p. 202, seq. 



28 OUTLINE OF THE 

mind can be engaged. If then it is to be taught 
as an Art, it should contain specific rules for reason- 
ing or thinking in every region of thought ; it must 
propose to itself nothing less than to enable men of 
the most various capacities to apply a set of princi- 
ples to effect the work of thinking correctly, under 
all circumstances. And the consequences are, an 
enormous expansion in the first instance, from the 
huge mass of heterogeneous materials ; and a con- 
sciousness of incompleteness in the second, since it 
is impossible to suppose that so vast a work has ever 
been completely achieved. Works in which the 
attempt has been made often contain a chapter on 
Scriptural Interpretation, and perhaps another on 
Forming a Judgment on Books : — can it be sup- 
posed that the precepts under either of these heads 
can be complete ? The one is an epitome of all 
Theology, and the other, it might be said, of all 
wisdom. Now Logic may be unquestionably an art 
or a science ; but it seems that all we can do is to 
lay down the principles of the science and leave 
each student to form for himself his own art, to 
teach himself how to employ these principles in 
practice. In this way we may attain something 
like completeness in a moderate compass, and may 
escape those incessant shiftings of the boundaries 
of the art, which are inevitable where men have to 
select a finite number of precepts out of infinite 
knowledge. 

§ 7. Those who represent Logic as both art and 
science are accustomed to assume that all arts, pos- 
sessing the principles of correspondent sciences, teach 
their application to practice, so that art is but science 



LAWS OF THOUGHT. 29 

turned to account. In the case of Logic this is not 
very far from the truth ; but as a general statement 
it is false, for it overlooks that notion of unconscious- 
ness which is commonly involved in Art. Shak- 
speare is admitted to be a consummate artist, but no 
one means by this that his plays were composed only 
to develop a certain express theory of Dramatic 
Poetry, such as Coleridge, Horn, or Ulrici have since 
founded upon them. No : the man of science pos- 
sesses principles, but the artist, not the less nobly 
gifted on that account, is possessed and carried away 
by them. " The principles which Art involves, sci- 
ence evolves. The truths on which the success of 
Art depends, lurk in the artist's mind in an undevel- 
oped state, — guiding his hand, stimulating his inven- 
tion, balancing his judgment, but not appearing in 
the form of enunciated propositions." * And because 
the artist cannot always communicate his own prin- 
ciples, men speak of his " happy art," as if it were 
almost by chance or hap that his works were accom- 
plished ; f and it was the fashion of the last century 
to speak of Shakspeare himself as a wild, untutored 
chUd of genius, not even to be named as an artist, 
because in truth his plays wanted dramatic science 
and were not obedient to' the law of the dramatic 
unities. So that the praise of being a good logician, 
or of having a logical mind, is sometimes awarded 
where there is little or no acquaintance with the sci- 
ence of logic. An understanding naturally clear, 
and a certain power of imitation, will enable the 

* WhewelVs Philosophy of Ind. Sciences, ii. p. 111. 

t So we have the line of Agalho, Texvi] rvxvv eareo^e, /cat tvx^ 



30 OUTLINE OF THE 

thinker or speaker to pour forth arguments which 
might serve for examples of all the logical rules, not 
one of which he has learnt ; and without some share 
of these talents, no precepts would avail to make a 
reasoner. But when we write upon Logic, the un- 
conscious skill of the artist must be left out of the 
account, because it cannot be communicated by rules. 
By the art of Logic we mean so much of the art of 
thinking as is teachable, and no more. The whole 
of every science can be made the subject of teach- 
ing.* 

§ 8. In treating of Logic as a science, we shall 
not forget that the ultimate object of the study is 
strictly practical, and shall labour to state the princi- 
ples in such a way as to facilitate to the student their 
application as an art. If we would redeem Logic 
from the charge usually brought against it, that it is 
a system of rules which the initiated never employ, 
and the uninitiated never miss, it must be by giving, 
it a far more extensive verification in practice than 
it usually receives. The inconsistency of teaching a 
science, where we mean that an art should be ulti- 
mately learnt, is only apparent, not real ; and at any 
rate is less injurious than that of those who teach an 
" instrumental art " which is never employed in prac- 
tice, and which is too often inadequate to the sim- 
plest tasks of practical application. 

§ 9. Ptire Logic is a science of the necessary laivs 
of thought. After the remarks already made (in page 
23), this subject will need less illustration. Logic only 
gives us those principles which constitute thouglit ; 
and presupposes the operation of those principles by 

* AidaKTTj nuGa kmaTTiin] donei elvai. Aristotle, Etli. Nk. vi. iii. 



LAWS OP THOUGHT. 31 

which we gain the materials for thinking. Thus I 
have a conception of house, which sums up and com- 
prises all buildings in which men live ; how did I ob- 
tain it ? Logic answers that it was generalized from 
different single houses which I had seen, by noticing 
what points they had in common, and by gathering 
up these common features into a new notion. It 
tells us, further, that this conception has various 
powers, that it may be defined, by declaring what I 
understand by it, that it may be divided, as into 
" houses of the rich," and " houses of the poor," that 
by comparing it with other general notions, as church, 
quay, monumental pillar, I may form a more general 
conception, in which all these may be comprehended, 
that of building. In all this Logic is to a certain 
extent my guide, because conception is one great 
function of thought ; but with considerable reserva- 
tions. It only tells me what is true of all concep- 
tions, and leaves me to apply the principles to this 
particular one ; for about houses Logic of course 
knows nothing, and to know what is a house and 
what not, I must go to Architecture or to common 
experience. Logic only tells me what principles I 
must put in practice in forming any general notion 
whatever; but to her all general notions are aKke. 
She makes no account of the great diversity of the 
classes of things they represent ; king, animal, acid, 
mammal, are all alike to her, and ranked together as 
conceptions, though the sets of objects they severally 
stand for have little resemblance. Logic then takes 
no account of the contents of a conception, of the 
things from which it is generalized ; these are contin- 
gent to her — if any given class from which a con- 



32 OUTLINE OF THE 

ception is now formed were annihilated, there would 
titiU be conceptions. The function of conception ia 
essential to thought ; its laws are accordingly laid 
down, but their particular use must be determined 
by the particular sciences. Logic teaches me what 
Generalization, or the forming of common notions 
from many things, is ; but Botany teaches me to gen- 
eralize upon plants. Political Economy upon the facts 
of social prosperity, Geometry upon the properties of 
space, and so on through the whole range of sciences. 
§ 10. In another direction also Logic seems to 
stop short, and to leave to another science what it 
was incumbent upon it to explain. Our conceptions 
are formed from single objects ; how do we come to 
know these ? The logician replies, that it is not his 
business to show how, but that for the most part they 
are derived from the senses, by means of which we 
are put in communication with the external world. 
But many further questions arise out of this answer. 
What are the senses ? How much of every notion 
conveyed by them is new, how much is the result of 
the experience of past impressions ? Does my sig-ht 
tell me that yonder steeple is about three miles off, 
or is it my understanding cooperating with my 
sight ? Is there no doubt that the senses report tru- 
ly ? Are we even certain that there is an external 
world ? To these and many like questions the logi- 
cian has one answer: "I presuppose a man able to 
perceive, to receive impressions from the sun'ounding 
world, and then merely explain the principles on 
which he must proceed, in combining his impressions 
and drawing inferences from them. The specula- 
tions you suggest are highly interesting, and all who 



LAWS OF THOUGHT. 33 

would understand the mind of man must enter upon 
them ; but the science of Metaphysics, or of the 
Human Mind, has ah-eady taken them up, and, closely 
connected as Logic is with this science, it is expe- 
dient that they should divide the ground. Logic 
therefore presupposes a mind capable of, and actually 
receiving, impressions ; though, perhaps, if there vjexe 
no such science as Metaphysics, it would be neces- 
sary even in a logical work to give a preliminary 
account of the origin of all knowledge." 

§ 11. Pure Logic is a science of the form, or of the 
formal laws of thinking; and not of the matter. The 
terms form and matter, in their philosophic use, will 
require some explanation. 

A statue may be considered as consisting of two 
parts, the marble out of which it is hewn, which is 
its matter or stuff, and the form which the artist com- 
municates. The latter is essential to the statue, but 
not the former, since the work might be the same, 
though the material were different ; but if the form 
were wanting we could not even call the work a 
statue. This notion of a material susceptible of a 
certain form, the accession of which shall give it a 
new nature and name, maybe analogically transferred 
to other natures. Space may be regarded as matter, 
and geometrical figures as the form impressed in it. 
The vrice is the matter of speech, and articulation 
the form. But as it is the form which proximately 
?n('i obviously makes the thing what it is (although 
there can be no form without matter), the word form 
came to be interchanged with essence and with 
nature. Already we have left the original sense a* 
some distance. 



34 ()UTLINE OF THE 

§ 12. With thinkers to whom the metaphorical 
sense was not so prominent, the word is used in three 
distinct but cognate senses. It is, 1st, a law or an 
idea, which are the same thing seen from opposite 
points. " That which, conteraplated objectiveli/ (that 
is, as existing externally to the mind) we call a Law ; 
the same contemplated subjectively (that is, as exist- 
ing in a subject or mind) is an Idea. Hence Plato 
often names Ideas, Laws ; and Lord Bacon, the 
British Plato, describes the laws of the material uni- 
verse as ideas in nature. Quod in naturd naturatd 
lex, in naturd naturante idea diciturP * Lava, heated 
metal, boiling water, the rays of the sun, aU rank 
under one common form (that is, law) of heatj 
namely : by which is meant that they, all and each, 
contain whatever is essential to heat. Lead, gold, 
vermilion, stones, and (in a greater or less degree) 
all bodies, possess weight ; the law of weight then 
is their form — the law under which they all come, 
the condition with which they all comply. By vir- 
tue of this form they are, not bodies indeed, but 
heavy bodies ; in other words, if we suppose that 
form or law to be expunged from the tables of the 
universe, their existence as to that nature or property 
would terminate ; or if the idea of weight were re- 
moved from the mind, we could no longer know 
thein as heavy bodies. 

§ 13. Now how does every one of the given in- 
stances come under the forms heat and gravita- 
tion ? By something contained within itself — by its 
embodying the law or definition ; that which comes 
under the form of weight must possess weight, must 
* Colei'idge's Church and State, p. 12. 



LAWS OF THOUGHT. 35 

have in it all that the definition of weight demands. 
A.nd here we may trace the second meaning of the 
word form : it is that part of any object through 
which it ranks under a given law. Every new object 
represented to the mind is referred to different laws, 
called forms, by virtue of various qualities in itself, 
each of which is termed metonymically, and with 
respect to the law under which it is the means of 
ranking the representation, its form. When we ob- 
serve (say) a stone, the mind proceeds to class the 
representation of it, afforded by the senses, under the 
various forms of colour, figure, size, weight, tempera- 
ture, &c. ; and with reference to the form (law) of 
weight, the weight of the stone would be its form 
(essential part), with reference to the form of colour, 
the grayness of the stone would be its. form. So 
that that, which in the object, when viewed in rela- 
tion to one law or form, is its form (essential part), 
is not its form when it is viewed in relation to an- 
other. Now the matter of any representation is that 
part of it which with reference to any given law is 
non-formal.* Thus in our stone, the weight, size, 
temperature, are parts of the matter, as far as the 
law of colour is concerned, for they are all non-for- 
mal, and the colour of the stone alone is formal. 
The matter is that which, when added to the form 
(essential part), gives it extraneity — outness — objec- 
tive f existence. Without something more than the 

* Hence the same thing is alternately form and matter. See Rit- 
ter's History, iii. p. 121 (Eng. trans.), for this point in Aristotle's doc- 
trine. 

t It will be well once for all to explain the modern use of the words 
subject and object — subjective and objective. The subject is the mind 
that thinks ; the object is that wliich it thinks about. A subjective 



36 OUTLINE OF THE 

mere form, there can be no instance of a law, an in- 
stance being the presence of the law in an object 
capable of containing it, and thus presupposing two 
things, the law and the capable object, whereof we 
term one the form and the other the matter. Ex. gr. 
triangle may be conceived by means of its own form 
or definition alone, but it must have a material part, 
it must become a triangle of stone, or wood, or ink 
on paper, as the condition of its external existence. 
When no separation, according to some law or other, 
of a representation into its formal and material part 
takes place, that is, where it is referred to no law or 
conception already in the mind, there must be total 
ignorance of the object represented ; the representa- 
tion miust remain obscure, and can never amount to 
a cognition. The absolutely material part of a cog- 
nition would be that which remains unknown after 
it has been brought under as many forms as the 
mind can reduce it to ; that which never becomes the 
condition of its ranking under a law. Forms have 
a triple mode of existence ; they exist in the Divine 
Mind as ideas, and are the archetypes of creation ; 

impression is one which arises in and from the mind itself; an objec- 
tive arises from observation of external things. A subjective ten- 
dency in a poet or thinker would be a preponderating inclination to 
represent the moods and states of his own mind ; whilst the writer 
who dwells most upon external objects, and suffers us to know little 
more of his own mind than that it has the power to reproduce them 
with truth and spirit, exhibits an objective bias. As the mind, how- 
ever, sometimes regards its own states, of feeling or sensation, as 
objects, it has been proposed to call them, when so emjDloyed, sidiject- 
objects, i. e. parts of the subject regarded as objects ; wliilst purely 
external things might be called objects. [Krug's Phil. Lexicon, under 
Gegenstand.) These words have undergone great changes of mean- 
ing, excellently traced out in Sir W. Hamilton's r.eid, p. 806, ia a note 
which only the Editor of that work could have written. 



LAWS OF THOUGHT. 37 

they exist as embodied in " instances " or examples, 
in which mode they are laws ; they exist, lastly, in 
the human mind as ideas ; thus they precede crea- 
tion, they are in it, they succeed it. 

§ 14. Writers of this school give yet a third sense 
to the word form ; as it denotes the law, so by an 
easy transition it stands for the class of cases brought 
together and united by the law. Thus to speak of 
the form of animal might mean, first, the law or defi- 
nition of animal in general ; second, the part of any 
given animal by which it comes under the law, and 
is what it is ; and last, the class of animals brought 
together under the Jaw. 

§ 15. The sense attached at the present day to the 
words form and matter is somewhat different from, 
though closely related to, these. The form is what 
the mind impresses upon its perceptions of things, 
which are the matter ; form therefore means mode 
of viewing objects that are presented to the mind. 
When the attention is directed to any object, we do 
not see the object itself, but contemplate it in the 
light of our own prior conceptions. A rich man, for 
example, is regarded by the poor and ignorant under 
the form of a very fortunate person, able to purchase 
luxuries which are above their ovjn reach ; by the 
religious mind, under the form of a person with 
more than ordinary temptations to contend with ; by 
the political economist, under that of an example of 
the unequal distribution of wealth ; by the trades- 
man, under that of one whose patronage is valuable. 
Now the object is really the same to all these observ- 
ers ; the same " rich man " has been represented under 
all these different forms. And the reason that the 



38 OUTLINE OF THE 

observers are able so to find many in one, is that 
they connect him severally with their own prior con- 
ceptions. The form then in this view is mode of 
knowing ; and the matter is the perception, or object 
we have to know.* Hence, when we call Logic a 

'* A few passages to illustrate these various meanings may be 
added here. Plato uses form in all the three senses, of law, distinc- 
tive or essential part, and species (which last word means form) ; as 
these places will show. 

" Eemember then, that I directed you not to teach me some one or 
two holy acts out of many, but that very form by which all holy acts 

are holy Teach me, then, the nature of that form itself, 

that looking to it and using it for our example, I may declare any of 
the actions of yourself or any other, which partake of this nature, to 
be holy, and any not so partaking, not to be holy." — Plat. Euthyp. 6., 
D. E. " And of the just, the unjust, the good, the evil, of all the 
forms, in short, the same holds true, that each is one and simple, but 
because everywhere appearing by incorporation with actions, or mat- 
ter, or other things, that each appears many." — Resp. 476, a. " For we 
have been accustomed to lay down one form for many particular cases, 
on which we impose the same name." — Resp. 596, a. "And accord- 
ing to the same form of justice, a just man will nowise differ from a 
just city, but will be like it." — Resp. 435, b. See also Sijmp. 205, d. ; 
Resp. 581, E. ; Polit. 258, E. Lord Bacon says, " The form of any 
nature is such that where it has place the given nature is also, as an 
infalhble consequence. Therefore it is ever present where the given 
nature is so, it attests that nature's presence, and is in it all. The 
same form is such that upon its removal the given nature infalh.bly 
vanishes. Therefore it is invariably absent where that nature is so, 
it in those cases disavows that natm-e's presence, and is in it alone." 
Nov. Org. II. 4. " The examination of forms proceeds thus. Con- 
cerning the given nature we must first bring together before the 
intellect all the known instances, agreeing in that nature, though 
manifesting it in vehicles {i. e. in matter] the most dissimilar." — 
Nov. Org. ii. 11. Again, " When we speak of forms, we understand 
nothing else than those laws and manifestations of the pure act, 
which order and constitute any simple nature, as heat, light, weight, 
in any sort of matter and subject that can contain them. Therefore, 
the form of heat or form of light, and the law of heat or hght, is the 
same thing, nor do we ever abstract our thoughts from actualities and 
active manifestations." — Nov. Org. ii. I'l. Again, "For since the 



LAWS OF THOUGPIT. 39 

science of the formal laws, or the form, of thinking 
we mean that the science is only concerred with 
that which is essential to, and distinctive of, the 
thinking process. Every act of thought is a thought 
about something ; it has matter as well as form. 
Every common noun is a sign of the act of concep- 
tion ; thus crystal is a conception formed from com- 
paring together many inorganic bodies which have 
spontaneously assumed certain regular forms • ani- 
mal, a conception from comparing many live crea- 
tures. Here the form is the same, for both are 

form of a thing is the very thing itself (ipsissinia res), and the thing 
no otherwise differs from tlie form, than as the apparent differs from 
the existent, the outward from the inward, or that which is con- 
sidered in relation to man from that which is considered in relation 
to the universe [or universal mind], it follows clearly that no nature 
can be taken for the true form, unless it ever decreases when the 
nature itself decreases, and in like manner is always increased when 
the nature is increased." — Nov. Org. ii. 13. 

Ritter in his EListory shows the analogy between form and differ- 
ence, matter and genus respectively, in the writings of Aristotle ; 
Plotinus indeed asserts their absolute identity. Ennead. ii. iv. 4. 
Por a collection of passages to illustrate Aristotle's doctrine, see 
Waitz' Organon. comm. on 94, a. 20. To our own great writers the 
philosophical senses of the word form were well known. Taylor, 
Andreives, Hooker, Berkeley, Butler, Sir Thomas Broiun, Coleridge — sup- 
ply instances which are now before us. But the subject has already 
occupied our attention long enough. Keckermann's Logic affords 
materials for understanding the views of the old logicians. 

The philosophic value of the terms matter and form is greatly 
reduced by the confusion which seems invariably to follow their 
extensive use. Whilst one writer explains form as " the mode of 
knowing" an object, another puts it for "distinctive part," which 
has to do with the being or nature of the thing rather than with our 
knowledge of it; where it means "shape" in one place, which is 
often a mere accident, in another it means " essence ; " so that it may 
be brought to stand for nearly opposite things. I will add, that 
probably there is no idea which these terms represent that cannot b« 
conveniently expressed by others, less open to confusion 



40 OUTLINE OF THE 

conceptions, and it is this quality which constitutes 
them thoughts ; but the matter is different, for one is 
about certain inorganic solids, and the other about 
living creatures. Logic, not being concerned with 
the things that thoughts are formed from, ranks the 
two together ; it is for Mineralogy and Zoology to 
distinguish between them. Logic only knows them 
for their formal or logical value. Are they concep- 
tions ? are they judgments, syllogisms, definitions, or 
genera ? Occupied only with the bare laws of 
thinking. Logic must leave to other sciences the 
consideration of the various matters upon which 
these laws operate. In these thoughts — "life is 
short " — " Mirabeau was said to have been poi- 
soned " — " the radii of a circle are equal," we have 
only one form or law of thinking, namely, Judg- 
ment, exhibited in connection with various things or 
matter. 

§ 16. Logic is said, in the language of the old 
writers, to be concerned only with second notions or 
intentions. The distinction between first and second 
intentions is connected with that which has been 
drawn between matter and form. Notions are of 
two kinds ; they either have regard to things as they 
are, as horse, ship, tree, and are called first notions ; 
or to things as they are understood, as notions of 
genus, species, attribute, subject, and in this respect 
are called second notions, which, however, are based 
upon the fijst, and cannot be conceived without 
them. The first intentions precede in order of time, 
for, as Boethius explains, men first intended to give 
names to things, before they intended to find names 
for their mode of viewing them. Now Logic is not 



LAWS OF THOUGHT. 41 

80 much employed upon first notions of things, as 
upon second ; that is, as we have said, it is not occu- 
pied so much with things as they exist in nature, but 
with the way in which the mind conceives them. A 
logician has nothing to do with ascertaining whether 
a horse, or a ship, or a tree exists, but whether one of 
these things can be regarded as a genus or species, 
whether it can be called a subject or an attribute, 
whether from the conjunction of many second no- 
tions a proposition, a definition, or a syllogism can 
be formed. The first intention of every word is its 
real meaning ; the second intention, its logical value, 
according to the function of thought to which it 
belongs.* 

* Vox articulata est signum conceptus, qui est in animo : duplex 
autem est ejusmodi vox, alia namque significat conceptum rei, ut 
homo, animal; aUa vero conceptum conceptus, ut genus, species, 
nomen, Terbum, euunciatio, ratiocinatio, et alise hujusmodi ; prop- 
terea hse vocantur secundje notiones ; illse autem primae. Zabardla 
de Nat. Log. i. x. 

Prima notio est conceptus rei quatenus est, ut animalis, homiais , 
secunda notio est conceptus rei quatenus inteUigitur, ut subjectum 
et attributum. Pacius. Anal. Comm. p. 3, A. 

See also BuJde {Aristotle, i. p. 432) ; Crackanihorp (Logic. Procem.) ; 
and Sir W. Hamilton in Ed. Eev., No. 115, p. 210. There is no 
autliority "W'hatever for Aldrich's view, which makes second inten- 
tion mean apparently " a term defined for scientific use ; " though 
with the tenacious vitaUty of error it still lingers in some quarters, 
after wounds that should hare been mortal. 



OUTLINE 



LAWS OF THOUGHT. 



LANGUAGE. 



" 'EcTTt /J£V ovv Tu ev ry (puvy tuv ev ry ipvx>3 ""(ZijT^iUarwv GvfijSohi.' 

Arist. cle Int. 

§ 17. 




ITHERTO we have assumed that the 
adequate object, matter of Logic is 
thought, rather than language ; that 
having explained the laws of thinking, 
it is not bound to examine under what conditions 
these manifest themselves in speech. But logicians 
do not invariably follow this course ; those who re- 
gard it as an act of reasoning, seeing that reasoning 
is not conducted but by language, and that many of 
the chief impediments to the coiTect performance of 
the process, lie in the defects of expression, make 
speech, and not thought, the matter with which 
they are primarily concerned. The name of Logic 
\tself would not be inconsistent with this view ; 
since log'os may mean the outer or the inner word — 



LAWS OF THOUGHT. 43 

the sermo mternus or the sermo extermis — the articu- 
late expression or the thought itself. Here then 
the relation between thought and language must 
be ascertained. 

§ 18. Language, in its most general acceptation, 
might be described as a mode of expressing our 
thoughts by means of motions of the organs of the 
body ; it would thus include spoken words, cries 
and involuntary gestures that indicate the feelings, 
even painting and sculpture, together with those 
contrivances which replace speech in situations 
where it cannot be employed, — the telegraph, the 
trumpet-call, the emblem, the hieroglyphic* For 
the present, however, we may limit it to its most 
obvious signification ; it is a system of articulate 
words adopted by convention to represent outwardly 
the internal proofs of thinking. 

§ 19. But language, besides being an interpreter 
of thought, exercises a powerful influence on the 
thinking process. The logician is bound to notice it 
in four functions : — (i.) as it enables him to analyze 
complex impressions, (ii.) as it preserves or records 
the result of the analysis for future use, (iii.) as it 
abbreviates thinking by enabling him to substitute a 
short word for a highly complex notion, and the like, 
and (iv.) as it is a means of communication. 



* Language is thus divided byM. Duval-Joiive, Logic[ue, p. 201. 

Absolute — Cries and Gestures. 
Conventional — Speech. 



Natural 



(Absolute — Painting and Sculpture. 
Conventional — Emblems, Telegraphic Signs 
Hieroglyphics, Writing. 



44 OUTLINE OF 'fHE 

§ 20. (i.) The language of words never records 
an impression, whether internal or external, without 
some analysis of it into its parts. Besides the ob- 
jects which we observe, and their qualities, we can 
reproduce in speech the mutual relations of objects, 
the relations of our thoughts to objects, and, lastly, 
the order and relation of our thoughts themselves. 
Now as the mind does not receive impressions pas- 
sively, but reflects upon them, decomposes them into 
their elements, and compares them with notions 
already stored up, language, the close-fitting dress of 
our thoughts, is always analytical, — it does not body 
forth a mere picture of facts, but displays the work- 
ing of the mind upon the facts submitted to it, with 
the order in which it regards them. This analysis 
iias place even in the simplest descriptions. " The 
bird is flying " is an account of one object which we 
behold, and in its present condition. But the object 
was single, w^hilst our description calls up two no- 
tions — " bird " and " flying," — and it is plain that 
this difference is the result of an analysis which the 
mind has performed, separating, in thought, the bird 
from its present action of flying, and then mention- 
ing them together.* In painting and sculpture, on 
the contrary, we have languages that do not employ 
analysis ; and a picture or statue would be called by 
some a synthetic^, or compositive, sign, from the no- 
tion that in it all the elements and qualities of the 
object which would have been mentioned separately 
in a description, are thrown together and represented 
at one view. The statue of the Dying Gladiator 
gives at one glance all the principal qualities so finely 
* See Mr. Smart's Sematology, cli. i. § 3. 



LAWS OF THOUGHT. _ 45 

analyzed by the following description, which, how- 
ever, includes also the poet's reflections upon and in- 
ferences from the qualities he observes ; the objective 
impression is described, but with a development of 
the subjective condition into which it throws the nar- 
rator.* 

" I see before me the Gladiator lie : 

He leans upon his hand — ^his manly brow 

Consents to death but conquers agony, 

And his drooped head sinks gradually low — 

And through his side the last drops, ebbing slow 

From the red gash, fall heavy, one by one. 

Like the first of a thunder-shower ; and now 

The arena swims around him — he is gone, 
Ere ceased the inhuman shout which haUed the wretch who won 

" He heard it, but he heeded not — his eyes 

Were with his heart, and that was far away ; 

He recked not of the life he lost, nor prize, 

But where his rude hut by the Danube lay : 

There were his young barbarians all at play, 

There was their Dacian mother — he, their sire. 

Butchered to make a Roman holiday ! 

All this rushed with his blood — shall he expire 
And unavenged 1 Arise ! ye Goths, and glut your ire ! " 

Bykon. 

Here the analysis of the impression is carried to its 
farthest ; and in the second stanza the object becomes 
quite subordinate to the inferences and fancies of the 
subject. But it is all the more striking as an illus- 
tration of the principle, that language presents to u« 
the analysis, as painting and sculpture the imitations, 
of a sensible impression. 

§ 21. But different languages are more or less ana- 
lytic, and the same language becomes more analytic 
* P. 25, note. 



46 . OUTLINE OF THE 

as literature and refinement increase.* This prop- 
erty indicates, as we should expect, corresponding 
changes in the state of thinking in different nations 
or in the same at different times. With increasing 
cultivation, finer distinctions are seen between the 
relations of objects, and corresponding expressions 
are sought for, to denote them ; because ambiguity 
and confusion would result from allowing the same 
word or form of words to continue as the expression 
of two different things or facts. Many ambiguous 
phrases, however, are suffered to remain, although 
the inconvenience of them must have been perceived 
from the first ; thus in Greek, the words v^ovai tckvuv 
bear the t^'^o opposite senses of " pleasures which 
children feel " and " pleasures derived from one's 
children," and in Latin metus hostium may mean 
either " the fear we have of our enemies," or " the 
fear our enemies have of us." In the Bible, words 
as important as " the love of God " express the pious 
regard we have towards our Father or his benignity 
towards his creatures. Prepositions are our inter- 
preters to clear away this confusion. Again, where 
the powers of a particular case of a substantive were 
once sufficient to denote the person whose action the 
verb described, whilst the pronoun was only used as 
an additional mark when great emphasis was re- 
quired, more modern habits, exalting the notion of 
personality, always assign a distinct word to the per- 
son. Thus the Greeks were able to express " I have 
a pain in my head " by three words, 'Myu lijv Ks^a'Af/v -. 
they needed no word to distinguish the person, and 

* See Donaldson, New Cratylus, b. i. ch. 3; Duval-Jouve, Logiqua 
p. 203 ; Damiron, Logique, p. 207. 



LAWS OF THOUGHT. 47 

merely qualified the verb by " the head," to express 
the seat of the pain. Our expression analyzes the 
verb into three distinct notions, " I," the person, 
" pain," the thing I suffer, and " have," the relation ; 
and shows more explicitly by the preposition " in " 
that the head is the seat of the pain. As a language 
acquires more of this character, and multipKes pro- 
nouns, prepositions, and conjunctions, it begins to 
forget its inflections, because it can express ail their 
powers by circumlocution with these new expletives. 
As syntax becomes more complex, inflections grow 
simpler. Our own language has almost lost the ter- 
minations of cases and persons ; and French writers 
attribute part of the clearness of their own tongue 
to the same cause, and to the consequent necessity 
of determining the relations of words clearly by 
proper connectives. The Greek has preserved its in- 
flections, although it has also acquired a full and 
complicated syntax ; which is owing probably to the 
fact that the Homeric poems moulded and set the 
former before the necessity for the latter had arisen. 
Perhaps the Greek of Homer shows more than its 
original complexity of syntax, from the touch of later 
editorial hands, like that of Peisistratus. Here then 
is a further use of language, and a proof of its inti- 
mate adaptation to thought. As the distinctions be- 
tween the relations of objects grow more numerous, 
involved, and subtle, it becomes more analytic, to be 
able to express them ; and, inversely, those who are 
born to be the heirs of a highly analytic language 
must needs learn to think up to it, to observe and 
distinguish all the relations of objects, for which they 
find the expressions already formed, so that we have 



48 OUTLINE OF THE 

an instructor for the thinking powers in that speech 
which we are apt to deem no more than their hand- 
maid and minister. 

§ 22. The superiority of spoken language over the 
language of painting and sculpture, has been the fre- 
quent subject of remark. One reason for it is that 
whilst the artist can only effect with certainty an 
impression upon the eye, and must depend upon the 
sensibility, often imperfect, of the spectators for the 
reproduction in their minds of the emotions that sug- 
gested his subject and guided his hand, the poet by 
his description can himself call up the appropriate 
feelings. Upon the forehead of the Dying Gladiator 
what chisel could inscribe plainly that which the poet 
bids us read there ? 

— "his manly brow 
Consents to death but conquers agony." 

In the picture of the Crucifixion at Antwerp, by 
Rubens, one of the most powerful specimens of " the 
brute-force of his genius," the action and purpose of 
more than one of the figures have been variously 
understood, and therefore by one party or another 
misunderstood. It is a disputed question whether 
the mounted soldier is looking with reverence at the 
chief Figure, or with cruel calmness at the agonies 
of one of the thieves ; and whether the soldier on 
the ladder has broken the legs of the thief, or is pre- 
paring to do so. Art finds few to understand its 
sweet inarticulate language ; but the plainer and 
fuller utterances of poetry cannot be misunderstood. 
Another reason of its superiority may be found in 
the greater power of words to suggest associations 



LAAVS OF THOUGHT. 49 

that knit up our present impression with others gain- 
ed from the past, or, better still, bring our emotions 
and moral feelings into connection with our present 
impression. What painting of a house can ever con- 
vey so much to a feeling heart as the short descrip- 
tion — " This is the home in which I spent my child- 
hood?" The sculptor raises a tomb, and covers it 
with the ensigns of piety and death, but his art tells 
us less after all than the brief inscription, " He died 
for his country," or, " he looks for immortality." * 
The painter cannot dip his pencil in the hues of the 
spirit ; the sculptor's drill and chisel cannot fix in 
matter the shapes which the mind assumes. The 
artist's thought remains unexplained, or depends upon 
the casual advent of congenial interpreters. In the 
comments upon our famous pictures and statues we 
have so many acknowledgments of the inferiority of 
the language of art to that of speech. Art would 
need no commentators, if it were thoroughly compe- 
tent to tell its own story. 

§ 23. (ii.) The second function we ascribed to lan- 
guage was that of preserving and recording our 
thoughts for future use ; nomina sunt notionum notce. 
A discovery can hardly be said to be secured, until it 
has been marked by a name w^hich shall serve to re- 
call it to those who have once mastered its nature, 
and to challenge the attention of those to whom it is 
still strange. Such words as inertia, affinity, polari- 
zation, gravitation, are summaries of so many laws 
of nature, and are so far happily chosen for their pur- 
pose, that, except perhaps the third, each of them 

* Compare Cousin, Philosopliie du Vrai, &c. le9on 27 ; and Burke, 
on the Sublime, § vii. 5. 
4 



50 OUTLINE OF THE 

guides us by its etymology towards the nature of the 
law it stands to indicate. When Gay-Lussac and 
Mitscherlich discovered that some chemical substan- 
ces either crystallize in the same form, or may be 
substituted for one another in compounds without 
change in the form which the compounds assume, 
they were not content with a statement of this beau- 
tiful and instructive law, but they invented the name 
of isomorphism (tendency to equal forms) to be an 
index and summary of the law and the experiments 
that illustrated it. When two opposite theories of 
medicine are termed Homoeopathy and Allopathy, 
these two compound words contain in fact an account 
of the opposing theories. A recent popular and in- 
structive book* has reminded us that it is possible to 
exhume from under the words that are their monu- 
ments, many a buried and forgotten theory. Thus 
we speak of a jovial, a saturnine or a mercurial tem- 
per, without remembering that this implies an ascrip- 
tion of its qualities to the planet Jove or Saturn or 
Mercury. Physiologists now ignore the systems from 
which such terms as animal spirits, good humour, 
vapours, proceed. But if words often serve as tomb- 
stones, and remain when the theory has mouldered 
away, they are as often the keys by which we unlock 
the casket of the living and precious discovery, to 
exhibit it to the -world. On the other hand, our emi- 
nent anatomist, Professor Owen, complains of the 
embarrassments produced in his science, by having to 
use a description where a name would serve; for 
instance, a particular bone is called by Soemmering 

* Trench on the Study of "Words, Parker, 1851. A logical student 
will find both amusement and profit in the little volume. 



LAWS OF THOUGHT. 51 

" pars occipitalis stricte sic dicta partis occipitalis 
ossis spheno-occipitalis," * a description so clumsy 
that we may be certain the bone will not be men- 
tioned more frequently than absolute need requires. 
In many cases, the privilege of giving the name 
which all the world shall employ, is conceded to the 
man or the nation who first clearly perceives the at- 
tributes, sees that they make one notion, and deter- 
mines how it shall be designated. We are indebted 
to the finer observation of the French for the names 
ennui, naivete, and finesse, for which we have given 
our own comfortable f in exchange ; and an English- 
man may notice with a smile of satisfaction that das 
gentlemanlike makes its appearance in a German 
author. 

§ 24. But it is not only in the higher laws of 
science, or the more subtle qualities which social 
refinement develops in men and in society, that the 
power of naming is the power of fixing the fleeting 
colours of thought. So long as we are cojitent w4th 
the bare reception of visual impressions, "we can in a 
measure dispense with words, because our remem- 
brance of the image of each object will serve instead 
of its name to ourselves, and a picture of it may 
represent it, though by a cumbrous and difficult pro- 
cess, to the minds of others. But thought never 
stops with the mere inspection of objects. In the 
simplest case, we proceed to decompose the sensitive 
impression into its parts. The tree which our eyes 

* See Owen on the vertebrate skeleton in Report of British AssO' 
ciation for 1846. 

t "Mot Anglais," says M. Philarete-Chasles (ix. p. 16), " ne d'un 
vieux mot Eranfais." But confortare is found in the Latin of the 
Vulgate. 



52 OUTLINE OF THE 

behold is found, upon reflection, to be tall or stunted, 
blooming or withered, old or young, straight or 
gnarled, waving in the wind or still ; and these 
properties have no independent existence, but are 
parts of the visible object; they are entia rationiSy 
and exist separately in the mind alone. Whence 
then, is our power of recalling them with such mar- 
vellous precision and facility ? How is it that we 
can keep them safely apart in the mind, instead of 
being obliged to look for them mingled and con- 
fused, in the objects from which we first disen- 
tangled them by reflection ? By virtue of the name 
we have attached to each of them ; which, like the 
labels upon the chemist's jars or the gardener's 
flower-pots, enable us at once to identify and secure 
the property we seek. Names then are the means of 
fixing and recording the result of trains of thought, 
which without them must be repeated frequently, 
with all the pain of the first effort.* 

§ 25. (iii.) Leibnitz was the first, so far as I know, 
to call attention to the fact that words are sometimes 
more than signs of thought ; that" they may become 
thoughts. His distinction between symbolical and 
intuitive [notative] conceptions f conducts us to 
the third function of language, that it abbreviates 
the processes of thought. Where our notion of any 
object or objects consists of a clear insight into all 
the attributes, or at least the essential ones, he would 
call it intuitive. But where the notion is complex, 
and its properties numerous, we do not commonly 

* Upon this, consult Damiron, Logique, p. 200, seq. and Duval 
Jouve, Logique, p. 199, seq. ; Mill on the Human ilind, vol. i. p. 83^. 
' Erdinann's Ed. p. 79. Acta Erudit. an. 1684. 



LAWS OF THOUGHT. oS 

realize all that it conveys ; the process of thinking 
would be needlessly retarded by such a review. We 
make use of the name commonly given to the no- 
tion as a symbol, even for ourselves, of all the prop- 
erties it possesses. A name then, employed in 
thought, is called a symbolical cognition; and the 
names we employ in speech are not always symbols 
to another of what is explicitly understood by us, 
but quite as often are symbols both to speaker and 
hearer, the full and exact meaning of which neither 
of them stop to unfold, any more than they regularly 
reflect that every sovereign which passes through 
their hands is equivalent to 240 pence. Such words 
as the state, happiness, liberty, creation, are too 
pregnant with meaning for us to suppose that we 
realize thek full sense every time we read or pro- 
nounce them. If we attend to the working of our 
minds we shall find that each word may be used, 
and in its proper place and sense, though perhaps 
few or none of its attributes are present to us at the 
moment. A very simple notion is always intuitive; 
we cannot make our notion of brown or red simpler 
than it is, by any symbol. On the other hand a 
highly complex notion, like those named above, is 
seldom fully realized — seldom other than symbolical. 
Here then is a farther use of names ; they serve to 
abbreviate the process of thought, as we have seen 
that they are useful in recording its results. And it 
may be noticed here that this distinction of cogni- 
tions throws a new light on the natm'e of definitioiis, 
or explanatory propositions, which are not, as they 
are often regarded, mere explanations to others of a 
meaning which we ourselves duly apprehend, but 



54 OUTLIXE OF THE 

are real acts of thought, which by unfolding before 
us some marks of our conception, partially or wholly 
unseen by us, have all the power of new truths even 
for ourselves. 

§ 26, (iv.) That language hath a fourth use, the 
most obvious of all, as the medium of communica- 
tion between mind and mind, needs no explanation. 
We might dispense with articulate speech for certain 
purposes, and might make gestures and changes of 
the countenance, which are the language of action, 
supply its place. But actions and the play of fea- 
tures, whilst they serve to express love or hatred for 
some present object, need of food or rest, joy or sor- 
row, can but express a very small and confined list 
of thoughts if we would indicate our feelings towards 
some absent person, or our wish for something at a 
distance, or direct attention to some inward state or 
sentiment; we cannot guide the thoughts of the 
spectator to the object present to our own mind, with 
any precision and certainty. Hence, it is necessary 
to appropriate to every object a signal, ahvays avail- 
able, which all men by a tacit convention accept as 
a substitute for the object, and which therefore recalls 
the object to the fancy whenever it is employed; 
and such a signal is a noun or name, defined by 
Aristotle to be " a sound which by convention is 
significant, but does not determine time." * The 

^ 'Ovofia jxlv oiiv karl <puv7j aTjjiavTLKfj Kara cvv&i]K.riv uvev xpovov, ijg 
UTjSkv jiepog earl ai]jj.avTiKbv KEXupi-c:/j,evov. — On Enouncement, ch. 2. 
(Tlie last words express that it divides into syllables only, and not 
words, otherwise it would be a sentence.) 'F7jfia (verb) 6e ean rd 
Kpnc arifialvov xpovov. — Ch. 3- /. C. Scaliger traced the distinction 
between the noun and the verb to a difference of time, for the noun 
represented a permanent thing, the verb a temporary and transi tovy 
state. 



LAWS OF THOUGHT. 55 

convention or agreement by which a whole nation 
confines a noun to one object or class of objects, is 
of course merely tacit ; whatever theory of the origin 
of language we adopt, we cannot suppose that a 
nation ever formally met and agi-eed upon the sev- 
eral names that should thenceforward express their 
various notions. Language is based upon general 
agreement, if we give our assent to its use every day 
by hearing and answering it, just as truly as if the 
view of Maupertuis were correct, that language was 
originally formed by a session of learned societies. 
Names however are representatives of things ; and 
the different states of things must find an expression 
likewise ; hence the need of adjectives and verbs. 
The verb has the power of assigning to the thing at 
a particular time the condition of being, doing, or 
undergoing something ; but as every verb may be 
resolved into an adjective-notion, and one particular 
word simply expressive of past or present or future 
state, as, for example, " he loved " is explained by 
" he was — loving," '^ he hopes " by " he is — hoping," 
we are justified in regarding all verbs as fundamen- 
tally one, the verb to be, with its three times or tenses 
of is, ivas, shall be, and their variety as arising from 
the incorporation of various adjective-notions with 
this simple verbal element. When two or more 
names come together, it is frequently necessary to 
express the mutual relation in which they stand ; a 
thing may be to, from, by, in, near, above, or below 
another, and prepositions are invented to determine 
this. Here then are the four principal parts of speech, 
substantives, or names to express substances, adjec- 
tives to stand for attributes, prepositions to denote 



56 OUTLINE OF THE 

relations, and a single verb to assign attributes oi 
relations to substantives at a determinate time.* 

§ 26. Aristotle's mode of arranging the classes of 
words admits of a brief, and (it may be hoped) in- 
telligible statement. Words are conventional signs 
of what takes place in the mind ; natm-al signs, as a 
scream to express terror, a scowl for hatred, a laugh 
for pleasant surprise, are not to be ranked among 
them. The question whether some sounds are not 
naturally more suitable to certain ideas, for examples, 
the sound of st to express strength and solidity, in 
stand, stout, sturdy, stick, stop, stubborn, or the 
sound of ivr to express turning with an effort, as in 
wring, writhe, wrest, wrestle, wrist, is passed over ; 
and it is evident that even if the sounds are suitable 
to the ideas they express, there was no necessity for 
adopting them, and they are, like the rest, subject to 
a tacit convention. Now some words, or rather 
vocal sounds, are simple, and consist of parts which, 
taken separately, have no meaning, or at least are not 
intended to have any in their present position ; such 
are the single sounds which we call words, as weapon, 
free, hardship, master, in which the components — 
ship and mast — have lost their proper meaning on 
entering into their several words. Some again are 
more complex, and are not only significant them- 
selves, but consist of significant parts ; these are 
what we call propositions or sentences, as The sun 

* See Condillac, Grammaire, cli. viii. The more advanced student 
will not fail to notice that as the ten Categories of Aiistotle answer 
to the parts of speech, so the simpler division of categories adopted 
by many later writers, into substance, attribute and relation, answers 
to three parts of speech. See below, the Section on Categories 



LAWS OF THOUGHT. 57 

has set. Following first the simple words, we find 
that some of them express a state or action at a 
given time, and are known as verbs ; others again 
are irrespective of time, and are called nouns. Of 
nouns, some have a sense independent of any auxil- 
iary words, and therefore can be employed alone as 
terms in a proposition, as city, wilderness, revenue ; 
others require the aid of other words to complete 
and determine their meaning, as — of a city, good, to 
Greece, which prompt the questions, ivhat part of a 
city ? Good what ? What happened to Greece ? 
and therefore are not complete in themselves. The 
former, properly speaking, are perfect nouns or names, 
but the latter, which include all cases of nouns except 
the nominative, are only parts of compound names, 
and require an addition to complete them. If a verb 
is added to one of the imperfect names, there will not 
be an intelligible sentence. Perfect names again 
might be either definite or indefinite, though the 
latter, which are nothing more than nouns with a 
negative prefix, as non-philosopher, are hardly worthy 
to be called names, both because they represent too 
large a number of objects, and because we explain 
them by saying what they do not mean. Turning 
now from simple words to propositions, we notice 
that some sentences are declaratory, as Ail must die ; 
others are only precatory or exclamatory, as " Oh 
that this too too solid flesh would melt I " Truth 
and falsehood, with the investigation of which Logic 
is concerned, belong only to the declaratory proposi- 
tions, and indeed these only can truly be called 
propositions. 



5S 



OUTLINE OF THE 



DIVISION OF WORDS. 

(See Aristotle on En. Ch. i. — iii.) 



Words 



' Whose parts have C Verbs ( Definite 

no meaning— J (" Perfect < 

simple AYords. ^^^^^^ ) (indefinite 
(. Imperfect 



Whose parts have 
meaning — sen- 
tences.- 



Declaratory — true or 
false propositions. 

Not declaratory, as a 
prayer or wish. 



§ 27. It is the province of Universal Grammar to 
examine the means of oral and -written communica- 
tion, and their laws ; and the hints here offered are 
rather intended to suggest than to supersede a further 
study of that science ; to which alone belong the de- 
tails of the doctrine of the Parts of Speech and their 
construction. Our business has been to point out 
the principal uses of language in aiding the process 
of thought. But great as these services are, it must 
not be supposed that an examination of the rules of 
language would answer every purpose of a logical 
system. As we are now constituted, our thoughts are 
invariably clothed in speech ; we use words even if 
we do not utter them. But if articulate speech were 
withdrawn from man, it cannot be supposed that 
thought w^ould for ever cease. On the contrary, 
wherever personal defects or external circumstances 
deprive the mind of this means of communication, 
it succeeds in providing an efficient substitute, and 
attains by practice much the same facility in the use 



LAWS OF THOUGHT. 59 

ol it as we enjoy in the exercise of the powers of 
speaking. Those among the deaf and dumb who 
have been taught by the pains of an enlightened 
humanity to converse and to think, must use, instead 
of the remembered words which we employ, the 
remembered images of hands in the various com- 
binations of finger-speech, as the symbols of their 
thoughts. The deaf and blind, taught the names of 
objects from raised letters, must think, not by asso^ 
ciations of sound, but of touch. The telegraph, and 
the signals on railroads, are new modes of speech ; 
and though 'an inexpert practitioner may have at first 
to translate such signs into common language, the 
skill which comes from practice soon prompts him 
to omit this needless intermediate step. The engine 
driver shuts off the steam at the warning sign, with- 
out thinking of the words to which it is equivalent ; a 
particular signal becomes associated with a particular 
act, and the interposition of words become super- 
fluous. Dr. Hooke, the inventor of the telegraph, 
called it " a method of discoursing at a distance, not 
by sound but by sight ; " and it is conceivable that 
we might learn to think by the telegraphic signals, 
so that " red flag over blue," seen with the eye or 
recaUed by the memory, might be our word for hap- 
piness. Leibnitz,* suggests the possibility of em- 
ploying various tones instead of articulate words to 
convey our notions ; and mentions that the Chinese, 
having a slender vocabulary, use the aid of tone and 
accent to vary and augment it. The Ranz-des- 
vaches that rends • asunder the heart of the Swiss 
sxfle, to him is but a word for " country and home ; '* 

* Nouv. Ess. iii. 1 



60 OUTLINE OF THE 

and the signet of the king sent to his servant, or the 
broken astragalus, by which the " guest-friend " re- 
minded his fellow of his plighted hospitality, are 
signs which plainly and certainly suggest thoughts, 
and therefore they are words also. Without thought, 
language would cease ; but we can conceive the 
language we use might be denied to us, and yet 
thought still proceed with the assistance of some 
other class of signs. And it is scarcely philosoph- 
ical to found an analysis of the reasoning powers 
upon that which, however useful to the reason, may 
be conceived to be universally, as it is now in isolated 
cases, separated from it, without destroying its ac- 
tion. Granting that the processes of thought may 
be traced to a great extent in the signs which it 
employs, they are still but signs, and if the process 
beneath them can be examined in itself — as we need 
not fear to maintain that it can — then to view it 
only in the instruments it uses is to leave our survey 
shallow and incomplete. Logic should expound the 
laws of thinking, and universal Grammar the laws 
of speech, apart from their special modifications in 
any given language. These two sciences would 
mutually illustrate each other ; whilst a clear separa- 
tion between them would probably have the effect 
of elevating the latter into an importance not hitherto 
assigned it. But no confusion can result from intro- 
ducing principles of language into Logic, as has 
been often done, so long as thinking is made the 
adequate object matter of the science, and language 
comes iri only as the minister of thought. 

§ 28. The question Ave have just considered — - 
whether thinking cpuld proceed without articulate 



LAWS OF THOUGHT. 61 

words as its signs — must be distinguished from the 
more difficult one — whether thinking could dispense 
with all signs. The latter we do not pretend to an- 
swer here ; but it may be hinted that thinking and 
science are not identical, that even if trains of syste- 
matic reasoning are quite beyond the reach of any 
but a speaking, " word-dividing " being, the simpler 
acts of thought may perhaps be within his reach. 
"Without language, all the mighty triumphs of man 
over nature which science has achieved would have 
been impossible. But this does not prove that man 
might not, without speech, observe objects, gather 
them into groups in his mind, judge of their proper- 
ties, and even deduce something from his judgment. 
Weak and incomplete the process of thought would 
be ; but we dare hardly say that one could not think 
at all. But in no subject is it more necessary to dis- 
tinguish between the actual, and the merely conceiv- 
able. Language and thought have never been put 
asunder, but in a few exceptional cases. With some 
nations they have the same name ; with all, the rules 
of the one are readily applied to the other. 

§ 29. The opinions about the origin of language 
may be divided into three classes, as follows. 

a. The belief that man at his creation was en- 
dowed with a full, perfect, and copious language, and 
that as his faculties were called forth by observation 
and experience, this language supplied him at every 
step with names for the various objects he encoun- 
tered. In this view, which has found many able 
advocates, speech is separated from, and precedes, 
thought ; for as there must have been a variety of 
ohenomena both outward and in his mind, to which 



62 OUTLINE OF THE 

the first man was a stranger, until long experience 
gi-adually unfolded them, their names must have 
been entrusted to him long before the thoughts or 
images which they were destined ultimately to rep- 
resent, were excited in his mind. 

b. The belief that the different families of men, 
impelled by necessity, invented and settled by agi*ee- 
ment the names that should represent the ideas they 
possessed. In this view language is a human inven- 
tion, grounded on convenience. But " to say that 
man has invented language, would be no better than 
to assert that he has invented law. To make laws, 
there must be a law obliging all to keep them ; to 
form a compact to observe certain institutes, there 
must be aheady a government protecting this com- 
pact. To invent language, presupposes language 
already, for how could men agree to name different 
objects without communicating by words their de- 
signs ? " In proof of this opinion, appeal is made to 
the great diversity of languages. Here it is supposed 
again that thought and language were separate, and 
that the former had made some progress before the 
latter was annexed to it. 

c. The third view is, that as the Divine Being 
did not give man at his creation actual knowledge, 
but the power to learn and to know, so He did not 
confer a language but the power to name and de- 
scribe. The gift of reason, once conveyed to man, 
was the common root from which both thought and 
speech proceeded, like the pith and the rind of the 
tree, to be developed in inseparable union. With 
+he first inspection of each natural object, the first 
Imposition of a name took place ; " Out of the ground 



LAWS OF THOUGHT. 63 

the Lord God formed every beast of the field, and 
every fowl of the air ; and brought them unto Adam 
to see what he would call them ; and whatsoever 
Adam called every living creature, that was the name 
thereof." (Gen. ii. 19.) In the fullest sense, language 
is a divine gift, but the power and not the results of 
its exercise, the germ and not the tree, was imparted. 
A man can teach names to another man, but nothing 
less than divine power can plant in another's mind 
the far higher gift, the faculty of naming. From 
the first we have reason to believe that the fmictions 
of thought and language went together. A concep- 
tion received a name; a name recalled a conception; 
and every accession to the knowledge of things ex- 
panded the treasures of expression. And we are 
entangled in absurdities by any theory which assumes 
that either element existed in a separate state, ante- 
cedently to the other. 

§ 30. It is impossible to trace the growth of lan- 
guage with certainty ; but it is most probable that 
many of the I'oots of the primitive language were 
originally imitations of the various sounds emitted 
by things in the natural world. A bird or animal 
perhaps received a name derived from, and resem- 
bling, its own peculiar utterance. The cry or excla- 
mation that man emitted instinctively under the 
pressure of some strong feeling, would be consciously 
reproduced to represent or recall the feeling on an- 
other occasion ; and it then became a word, or vica- 
rious sign. Where natural sounds failed, analogy 
would take the place of imitation ; words harsh and 
difficult to pronounce would be preferred to stand 
for unpleasing objects, over those of a more bland 



64 OUTLINE OF THE 

and facile character, which would be appropriated to 
pleasant things and conceptions. Mere agreement 
among those who used the language, would be suffi- 
cient to stamp a vocal sound as the name of a cer- 
tain object, where neither imitation nor analogy sug- 
gested one. But these original roots, the simplest 
form of substantives, would gradually become less 
and less discernible as the language grew richer and 
more intricate. Wherever new arts are practised, 
we may easily find opportunities of watching the 
growth of new names for its instruments and pro- 
cesses, guided by these three principles, imitation, 
analogy, and mere convention. 

§ 31, The various parts of speech took their origin 
from the noun and verb, or possibly from the noun 
alone.* Many instances can be found of adverbs 
and prepositions which are distinctly substantives, 
and of conjunctions which are but parts of verbs. 
Then the close connection between the verb and 
noun is indicated by the number of words which, 
in our own language, are both verb and noun, 
and only distinguished by mode of pronunciation. 
Inflexions perhaps originated in the addition of one 
word to another, so that the terminations of nouns 
and verbs are in reality distinct words incorporated 
with them. These are but slender hints of the 
direction in which profound and acute researches 
have been made. And I do not think that such 
attempts to dissect and analyze language, pursued 
with proper caution, tend at all to lower our esti' 

* " Omnes Hebreaj voces, exceptis tantura interjectionibus et 
conjunctionibus, et una aut altera particula, vim et proprietates 
pominis habeiit." — Spinosa, Gram. Heb 5. 



LAWS OF THOUGHT. 65 

mate of the importance of the gift of speech, ov of 
its marvellous natra-e. It is not more wonderful 
surely that the Giver of Good has endowed man 
with a complete language, than that He has en- 
dowed him with faculties which out of the shrieks 
of birds in the forest, the roar of beasts, the murmur 
of rushing waters, the sighing of the wind, and his 
own impulsive ejaculations, have constructed the 
great instrument that Demosthenes and Shakspeare 
and Massillon wielded, the instrument by which the 
laws of the universe are unfolded and the subtle 
workings of the human heart brought to^ light. But 
in no line of inquiry is caution more necessary, are 
deductions more likely to be fallacious. It does not 
follow that a word as we use it now bears a gross, 
narrow or material sense, because the root to which 
we can refer it had a limited meaning, and was 
connected with matter. If truth according to its 
etymology means that which we trow or think, ac- 
cording to long usage it means that which is certain 
whether we think it or not ; if spirit meant origin- 
ally no more than breath, it has so far left that sense 
behind, that when the breath is exhaled the spirit 
remains immortal.* 

^ On the origin and growtli of Language, see Herder Ursprung 
des Spraches (a prize Essay) ; Ranch's Psychology, New York, 1840; 
T'ooJce's Diversions of Purley ; Harris's Hermes ; Donaldson's New 
Cratylus ; Mansel's Prolegomena, p. 17 ; Cousin, Frag. Philos. on 
Maine du Biran; Duval-Jouve, Logiqiie, §§ 189, seq. ; Plato's Qat^lus. 
6 



OUTLINE 



LAWS OF THOUGHT. 



INTRODUCTION. 



CONCLUDED. 



" Hujus discipline studium atque cognitio in principiis quidem 
tetra et aspernabiiis insuavisque esse et inutilis videri solet : sed nbi 
aliquantum processeris, turn denique et emolumentum ejus in animo 
tuo dilucebit, et soquetur quiEdam discendi voluptas insatiabilis." — 
AuLus Geli.ius. 



§32. 




OGIC has been called an a priori science. 
The distinction between truths a priori 
and truths a posteriori, as observed uni- 
versally by modern writers, may be drawn 
as follows. If there are any truths which the mind 
possesses, whether consciously or unconsciously, be- 
fore and independent of experience, they may be 
called a priori truths, as belonging to it prior to all 
that it acquires from the world around. On the other 
hand, truths which are acquired by observation and 
experience, are called a posteriori truths, because 
they come to the mind after it has become acquainted 



LAWS OF THOUGHT. 67 

with external facts. How far a priori truths or ideaa 
are possible, is the great campus philosophorum, the 
great controverted question of mental philosophy. 
In entering into it, and that only so far as our pres- 
ent purpose requires, we must remove from it one 
great cause of misunderstanding. No one at present 
maintains that the mind can know any thing at a 
point of time before its observation of external 
things began; a mind in that condition would be 
full of thick darkness. However independent of ex- 
perience any process may appear to be now, as for 
instance that by which geometrical truths are proved, 
we may be sm*e that we made much use of observa- 
tion before we educed the very laws which place it 
in our minds far above all need of confirmatory 
evidence from observation. A mind which never 
observed, would not be a mind. But the question 
is whether even the facts which we observe do not 
furnish evidence that something has been in the 
mind before it was directed to the facts ; just as we 
know by looking at something that we have eyes, 
and must have had them before we looked, although 
without putting them to their proper use we could 
never have known that we had them at all.* Now 
without going into the dispute as to how much of 
our knowledge is a priori, we may be able to show 
that at least the conditions of all knowledge are so, 
— that the mind does not simply reflect the images 
of things without, but impresses characters of her 
own upon them, — that our knowledge of things is 
not the exact counterpart of the things, but of the 
things and the mind operating together. When we 
* Coleridge, Lit. Rem. i. 326 ; and Friend, i 307, note-. 



68 OUTLINE OF THE 

see our image in a mirror (to use Bacon's simili- 
tude), we know that our shape is the cause of it on the 
one side and the power of reflection in the mirror on 
the other ; if we were to see it multiplied, or in- 
creased, or diminished, or changed in hue, we should 
infer that the mirror had several angular faces, or 
was concave, or convex, or made of tinted glass. 
Each of these properties would be inherent in the 
mirror prior to our presenting ourselves before it; 
they are its a priori laws ; although we could only 
ascertain them a posteriori, by a trial. When an 
image is received upon the mirror of the mind, we 
see that the latter also has its laws and properties. 
Our remark upon one object of common occurrence 
is " the bird is flying against the wind." Have we 
here no more than the single object which the eye 
presents ? There are three distinct notions, of a 
bird, of its being in the act of flying, of the direction 
of its flight ; so that the mind has decomposed the 
one object into three impressions ; and there is be- 
sides an act of deciding upon the agreement of these 
impressions, expressed by the word " is." And as 
the object does not resolve itself into three parts, 
but is to all intents and purposes one, and as there 
can be nothing in the object to correspond to the 
act of judging expressed by the word " is," we con- 
clude that the power of analysis of the simple im- 
pression into three, together with that of judging 
upon it, belong to the mind itself. Further, as we 
have no reason to think that this object created the 
two powers, or did more than call them into action, 
we conclude that they were jDresent a priori, that 
is, prior to the impression from without. And again, 



LAWS OF THOUGHT, 69 

for the same reason that they are not found in this 
object of sense, — that is, because they decompose it 
into many parts and judge upon its parts, which no 
object can do for itself — we conclude that they were 
not learnt from any object we may have seen before ; 
and therefore they are absolutely a priori, they are 
independent of all experience.* 

§ 33. Hence we may understand the importance 
which attaches to Leibnitz's well-known comment on 
the maxim of the school of Locke f ; to the nihil est 
in iiitellectu, quod nonfuerit in sensu, he adds — nisi 
intellectus ipse. The mind does not simply receive 
the impressions of the senses, like the passive surface 
of a mirror ; it groups them, judges about them, sep- 
arates their qualities from each other, and draws in- 
ferences about the qualities which like objects, hitherto 
unknown, may be expected to have. But qualities, 
classes, inferences, are not objects of sense, however 
they may reside in or be drawn from .those objects. 
They have no separate existence out of the mind; 
whilst, within it, they are perfectly distinct. This 
transmutation of objects of sense into their elements 
must therefore be the work of the mind alone. It is 

* The various modes of expressing tlie antithesis between thoughts 
and things are here exhibited in a tabular form : — 



Man, 

Thoughts, 

Theories, 


as opposed 


to Nature 
Things 
Facts 


Reflection, 

Subject, 

Form, 




Sensatic 

Object 

Matter. 



Wkewell's Phil, of Lid. Sci. vol. i. b. i. 
t Leibnitz, Noitveaux Essais, ii. i. p. 223, Erdmatin's Ed. Loclce him- 
self admits "ideas of reflection," gained by observing the mind's own 
actions, besides "ideas of sensation," On Hum. Z'nder. ii. v. 1. 



70 OUTLINE OF THE 

a law of the intellect itself, and never was nor can 
have been in the sensuous impressions we have re- 
ceived. 

§ 34. Pure Logic treats only of those laws or con- 
ditions to which objects of sense are subjected in the 
mind ; and hence it is called an a priori science. It 
unfolds the laws of the intellectus ipse, and gives no 
account of the representations of the senses as such. 
It will enumerate, for instance, all the different kinds 
of judgments which can be formed, but will not pre- 
tend to decide upon the truth of any one judgment 
respecting something which is now before the eyes. 
As the laws of the understanding are few and inva- 
riable, whilst the phenomena in the v/orld around us 
appear, from our imperfect knowledge of their com- 
plicated laws, very uncertain. Logic is far less liable 
to error than those sciences which have to do with 
external facts. Thus the truth that " if A is B and 
B is C, then A must be C," cannot bs denied, what- 
ever we suppose these letters to represent. The for- 
mula is universal and necessary ; it was so in the days 
of Aristotle, and will be as long as there remains 
upon the face of the world one mind to think. But 
an a posteriori science — a science of external facts — 
like Astronomy, though using demonstration, depends 
upon observation, and the accuracy of its calculations 
is in a direct ratio to our opportunities of observing 
all the circumstances which may affect them. It can 
never be a necessary truth that after each interval of 
two hundred and twenty-three lunations the sun ^vill 
be eclipsed : grounded only upon facts, whenever 
some convulsion shall be prepared by the Creator to 
disturb them, its prediction will fail. Calculations 



LAWS OF THOUGHT. 71 

of the period of the return of comets have sometimes 
failed, because of our defective means of observa- 
tion ; thus the return of the comet of 1770 was prom- 
ised in five years and a half; it falsified the predic- 
tion, and never returned at all. 

This view of Logic as an a priori science, it is 
hoped, will meet with a pretty general assent ; and 
we purposely abstain from touching the great ques- 
tion of Metaphysics — how much of our knowledge 
is from the mind itself and how much from experience. 
The conflicting opinions upon this matter will never 
be reconciled, and perhaps the best service which 
philosophy could receive would be rendered by mark- 
ing out the region which must be mutually ceded by 
the opposite schools.* 

§ 35. By explaining some of the various names 
bestowed on Logic by those who have treated it, we 
shall have a clear view of the position they intended 
it to occupy, (a.) It has been called the Architec- 
tonic Art, by which is meant that it occupies the 
same position with regard to the sciences and arts in 
general, that Architecture does to the labors of the 
carpenter, the mason, the paviour, the plumber and 

* Before leaving the subject, it must be noticed tliat the term a 
priori has undergone important changes of meaning. In Aristotle's 
philosophy the general truth is "naturally prior" (■nporepov ry Avaet) 
to the particular, and the cause to the effect ; but since we know the 
particular before the universal, and the effect before we seek the 
cause, the particular and the effect are each "prior in respect to us " 
(■rrpo-spov npog vfxdg). Anal. Post. I. ii; Top. vi. iv. ; Metaphys. v. (A) 
xi. p. 1018. Ed. Berol. roUowing this, the Schoolmen call the argu- 
ment which proceeds from cause to effect, a priori demonstration. 
But with Hume (Skeptical Doubts) a priori has the sense given in the 
text, which Kant has fixed in the language of philosophy. See 2ren- 
ddenburg's Excerpta, p. 81, Ed. iii. ; Sir W. Hamilton's Reid, p. 762 



72 OUTLINE OF THE 

the glazier; arranging and directing them indeed so 
as to contribute to one common end, but not neces- 
sarily knowing the details of their business, nor put- 
ting its hand to their toil. Used by Plato as an illus- 
tration {Polit. 259, E.) the word Architectonic was 
adopted by Aristotle as a general name for aR arts 
which kept other arts subservient to them (Eth. Nic. 
I. i.). And as the rules of Logic must be obeyed 
not by one art or the other but by every one, other 
writers were natm-ally led to apply the name Archi- 
tectonic to it especially. The same supremacy is 
vindicated to Logic in another of its names ; by the 
followers of Aristotle it was called (b.) the Instru- 
ment (or Organon) and the Instrument of Instru- 
ments. Aristotle himself did not affix the name of 
Organon to that collection of logical treatises that 
now bears the name ; but he speaks of our possess 
ing in ourselves two instruments {bpyava) by which 
we can employ external instruments, the hand for 
the body and reason for the soul ; and adds that sci- 
ence is the instrument of reason;* and it is probable 
that Alexander and John Philoponus were led by 
these and similar expressions to apply to the laws of 
reasoning, as displayed in the two " Analytics " of 
their master, the name of the " Instrument," or Or- 
ganon. Once affixed to these treatises, it was soon 
extended so as to embrace all the works that are 
now included under it. Elsewhere Aristotle calls 
the hand of man " an instrument before instruments" 
and " an instrument of instruments," and again com- 
pares the mind to the hand, so that to transfer this 

* Arist. Prohl. A. 5, (955, b.) De An. V. 8, (432, a. i.) Polit. A. 3, 
(1253, b.) 



LAWS OF THOUGHT. 73 

compound title also to Logic is just as agreeable to 
the master's mode of expression. Because the rules 
of Logic are employed in every scientific inquiry, 
Logic may well be called emphatically the instrument 
of the mind, just as the hand is the instrument em- 
ployed before all others in every act with which the 
body is concerned. Further, just as a hand wielding 
a spade may be considered an instrument with an 
instrument, so may Logic when directing the proce- 
dure of another science (and where is the science it 
does not direct ?) be regarded as an instrument with 
an instrument. By its title of Architectonic we re- 
cognized Logic as the chief or master-science ; by 
the title Instrument of Instruments we assert that it 
is the science next and nearest to the mind itself, by 
which it handles, as it were, the other sciences. Some 
logicians of eminence indeed refuse to give Logic any 
other title ; thus Zabarella [de Nat, Log. i. x.) denies 
that it is either an Art or a Science or a Faculty in 
the proper sense, and affirms that the name of Orga- 
non is alone applicable to it. Other names which 
establish the preeminence of Logic over the real sci- 
ences will not require any explanation ; such are (c.) 
the Art of Arts {ars arfium), (d.) the System of Sys- 
tems [disciplina disciplinarum) , (e.) the Key of Wis- 
dom, (f ) the Head and Crown of Philosophy [caput 
et apex pliilosophice). But these swelling titles must 
not lead us to forget that if Logic is the highest sci- 
ence of all, it is also the servant of all ; if it is the 
widest in its scope, it is also by itself the most bare 
and fruitless ; it gives no knowledge of things, for it 
is an instrumental and not a real science, and only 
when working in conjunction with sciences of hum- 



74 OUTLINE OF THE 

bier style and pretensions can it further the interests 
of philosophy or add to the stock of useful knowl- 
edfi^e. — As it offers rules for seekina: after truth it has 
been called (g.) Zetetic or the Art of Seeking ; as 
these rules are not given in vain, we may regard it 
also as (h.) Heuristic or the Art of Discovering Truth. 
As it cures, the mind of prejudices and errors, it is 
called (i.) Medicina Mentis, and (k.) the Cathartic of 
the Mind. Logic, upon a lower view of its preten- 
sions, as teaching the right use of the faculties in the 
discussion of any question, with or without the pur- 
pose of attaining truth, is called (1.) Dialectic* The 
name of (m.) Canon was given by Epicurus to the 
Logic of his school, though, if we may trust Diogenes 
and Cicero, it was a very different system from, and 
much more free from technical details than, the Logic 
in general use. But in the sense of a rule by which 
thoughts are to be gauged and measured, to secure 
their truth and correctness, it may be applied to any 
view' of logical science. 

§ 36. Uses and pretensions of Logic. The acts of 
the mind are so quick, so numerous, so complex, that 
they are not easy to note and describe, although we 

* With Aristotle, Analytic teaclies tlie formal laws of thought, 
which philosophy applies to the discovery of truth ; Dialectic (as 
taught in the "Topics") is a popular application of these laws to dis- 
cussion and the defence of a proposition, rather than to the attain- 
ment of truth, although it makes attempts in that direction ; Rhetoric 
closely resembles Dialectic, in using popular forms of argument and 
in postponing truth to some lower aim, only that the aim of the 
former is to wor"'?: conviction in the intellect, that of the latter to per- 
suade, through the intellect and the moral nature combined ; Sophistic 
is like Dialectic, except that it seeks to mislead imder pretence of 
convincing us of a truth, and so impUes a wrong moral bias ; and 
Eristic is the art of disputing cleverly so as to put an adversary to 
eilence. 



LAWS OF THOUGHT. 7o 

paily perform them, and that without serious mistake. 
Logicians have generally erred on the side of under- 
rating the number both of the mental processes them- 
selves, and of the particular acts which go to the at- 
tainment of any judgment or conception. As the 
act of standing erect, so simple apparently, calls into 
operation a numerous array of muscles, by means of 
which the body perpetually sways and adjusts itself, 
without conscious effort, so we may believe that the 
mind goes through acts, which from long practice 
scarcely awaken her own attention, much less the 
sense of pain and effort, yet which involve a great 
number of subordinate acts, depending on distinct 
principles. And as it takes the physiologist many 
pages of explanation to analyze a posture which a 
three-years' child assumes and retains without diffi- 
culty, so the logician seems to spend too many words 
upon the rules of thinking, since all men, from the 
statesman to the clown, are able to think, whethei 
they have learnt rules or not. To show that the 
complexity we speak of, really belongs to thoughts 
apparently very simple, we may examine an example. 
When Captain Head was travelling across the Pam- 
pas of South America, " his guide one day suddenly 
stopped him, and, pointing high into the air, cried 
out ' A lion ! ' Surprised at such an exclamation, ac- 
companied with such an act, he turned up his eyes, 
and with difficulty perceived, at an immeasurable 
height, a flight of condors soaring in circles in a par- 
ticular spot. Beneath this spot, far out of sight of 
himself or guide, lay the carcass of a horse, and over 
that carcass stood, as the guide well knew, a lion, 
whom the condors were eyeing with envy from their 



76 OUTLINE OF THE 

airy height. The signal of the birds was to him 
what the sight of the lion alone would have been to 
the traveller, a fall assurance of its existence.'** 
Here was an act of thought which cost the thinker no 
trouble, which was as easy to him as to cast his eyes 
upward, yet which from us, unaccustomed to the sub- 
ject, would require many steps and some labour. 
The sight of the condors convinced him that there 
was some carcass or other; but as they kept wheel- 
ing far above it instead of swooping down to their 
feast, he guessed that some beast had anticipated 
them. Was it a dog or a jackal ? No ; the condors 
would not fear to drive away, or share with, either; 
it must be some large beast ; and as lions abounded, 
or had been seen in the neighbourhood, he concluded 
that one was here. These steps of thought at least, 
and probably many more, rushed through his mind 
with the proverbial swiftness of thought, but they 
were summed up in the words " A lion." Daily and 
hourly we run through similar or more complicated 
trains of thinking, with no more consciousness of the 
several links than the organ-player has of each note 
he strikes in a rapid passage of full harmony. As 
the logician professes to give an account of the think- 
ing process, he must try to follow all these out, and 
show the laws on which they severally depend. He 
may incur the charge of tediousriess in showing (for 
instance) that our notion of "house" is formed by 
the successive steps of Comparison, Reflection, Ab- 
straction, and Generalization, for every one has been 
forming such general notions all his life without 
knowing one of these hard names ; or that " he will 

* Sir J. Herschel's Prelim. Discourse, p 84. 



LAWS OF THOUGHT. 77 

come, for he said he would," contains three terms and 
three propositions, joined together by a sign of in- 
ference, which constitutes them a syllogism ; for we 
can all manage our inferences without these formali- 
ties. Bat still he must not shorten his explanation 
at the expense of truth ; these are laws of thought, 
and it is his business to ascertain them, just as the 
physiologist thinks himself bound to examine all the 
laws of the bodily motions and positions so uncon- 
sciously assumed. But is there any gain to mankind 
from this analysis ? Would not natural logic suffice, 
without a number of technical rules, uninviting to 
learn, hard to remember, and seldom applied ? What 
is the use of Logic ? — I answer, that knowledge itself 
is a use, and that all legitimate inquiry rewards itself 
with its own pleasures. The appetite for finding out 
laws from facts, causes from effects, necessary truth 
from fleeting occurrences of the day, puts in its claim 
to gratification, which is as legitimate, if less impe- 
rious, as that of the animal nature for food and sleep. 
The studies which enwrapt the soul of Archimedes 
in the siege, of Aquinas at the royal feast, of Joseph 
Scaliger during the massacre of Saint Bartholomew's, 
must have been a source of pleasure, pure and high, 
from which they had a right to draw. If the ques- 
tion, what "fruit" does it bring? — which the Baco- 
nian philosophy puts so often — be understood, as it 
certainly ought not, to refer only to the material 
wants and comforts of humanity, it is a base, sordid, 
and stupid question, against which every better mind 
indignantly protests. Science was never brought to 
its present height by hopes of wealth, plenty, and 
comfort alone, but chiefly by those mirabiles amores 



78 OUTLINE OF THE 

with which she can inspire her followers. He v\'ho 
loves to see the processes of his mind reduced to 
their laws and causes, to him are logical studies a 
pleasure — to him they bring fruit. 

§ 37. But whilst even the coldest followers of 
Bacon * admit that the value of science must not be 
estimated by what she can actually perform, no doubt 
it must be granted that even the highest sciences do 
condescend to help our lowest wants. Astronomy, 
Chemistry, Geology, and Mechanics not only furnish 
delightful contemplations to the student, but they 
put food into the mouths of the vulgar ; they clothe 
them, and fill their purses, they put houses over their 
heads, and adorn them with objects of beauty and 
convenience. Logic has its use also in improving the 
condition of men ; it teaches, or perhaps I may only 
say, may be made to teach, them to think. This is 
often denied, and partly on account of the extrava- 
gant claims put forward by logicians, who assume 
that the acquisition of a few logical rules will enable' 
men to think correctly, just as the possession of a 
watch enables them to ascertain the hour. No 
science can make such pretensions. The active in- 
tellect has two parts, one of which originates our 
thoughts, and may be called the suggestive, whilst 
the other checks and judges thoughts as they arise, 
and may be called the critical, power. Thoughts are 
continually suggested without the consent of the 
will. One would think indeed, were it not for the 
obvious similarity these spontaneous visitors bear to 

* See M. Comte, Pliilosophie, iii. p. 280, as against the brilliant but (I 
think) mistaken view of Bacon and the old philosophers, in il/acau- 
lay's Misc. Essays. " Bacon." 



LAWS OF THOUGHT. 70 

the matter of former study, that they were in no 
sense our own, that an independent being, over 
whom one had absolutely no control, was whisper- 
ing within us. In the poetical temperament, where 
the power of suggestion strongly predominates, the 
thoughts which arise are less like any thing one re- 
members, than in ordinary minds ; and hence poets 
have maintained, perhaps in full sincerity, that an 
unseen spiritual power, higher than themselves, used 
them as the channel of its teaching, — that they were 
inspired.* The suggestive power may be educated as 
certainly as, though more gradually than, the critical. 
The discovery which we call a flash of genius, a 
happy thought, really depends as much upon pre- 
vious acquirements, as the power of stating a case 
or applying a rule does. These bright suggestions 
never occur to the ignorant ; f they have the facts 
before them, but their imaginations are not trained 
to leap to the proper inference from them. All dis- 
cipline of the suggestive must proceed from the criti- 
cal power ; it is by a long, careful, patient analysis of 
the reasonings by which others have attained their 
results, that we learn to think more correctly our- 
selves. He who reads over a work upon Logic 

=* Plato again and again mentions this claim of poets. See Ion, 
533 ; D. Apol. Soc. 22 ; B. C. Legg. 719 ; C. Meno, 99 ; B. C. Phcedms 
245. A. Stallbaum [Preface to Ion) does not think that Plato would 
neny to the poet a modifying power over the dictating principle. But 
the truth is, Plato still allows them all they claim, in order that the 
want of independence {avroTzpayia) may be seen and despised. Com- 
pare Ovid (Fasti, vi. 5.) ; Cicero {de Div. i. 37.) ; Morgenslern (de Rep. 
p. 296.). Dictation and inspiration are distinguished. Coleridge't 
Table Talk, ii. 30. 

t See this beautifully illustrated in Whewell, Phil. Ind. Sci. B. xi 
5 5. And below, the section on Anticipation. 



80 OUTLINE OF THE 

probably thinks no better when he rises up than 
when he sat down ; but if any of the principles 
there unfolded cleave to his memory, and he after- 
wards, perhaps unconsciously, shapes and corrects 
his thoughts by them, no doubt his whole powers of 
reasoning gradually receive benefit. Perhaps the 
principal advantage which science has received from 
Bacon's great work has arisen from his denounce- 
ment of hasty generalization,* which being easily 
remembered, and applicable to all subjects, has much 
influenced the practice of all scientific students. In 
a word, every art, from Reasoning down to Riding 
and Rowing, is learnt by assiduous practice, and if 
principles do any good, it is proportioned to the 
readiness with which they can be converted into 
rules, and the patient constancy with which they 
are applied in all our attempts to excel. 

§ 38. No one will pretend to say that Logic has 
been fairly treated in this respect. Our view of the 
elements of Logic has indeed been very imperfect, 
and would be quite insufficient for scientific analysis ; 
but no attempt has been made to widen and improve 
it, because we have not tried to put it to use, and so 
found out its inadequacy. In some popular treatises, 
of latest date, both English and French, the rules of 
syllogism are passed lightly over, as rusty weapons 
that have no place in the armory of science — " You 
will find them somewhere — in Aristotle, in the 
Schoolmen, or in Manuals ; — we admit their exist- 

^ Nov. Organ, i. 19, 20, 22. Not that Bacon first discovered this 
abuse of the law of Anticipation. Plato knew it well enough [Fhile- 
bus, 16, E. ol 6s vvv K. T. A.), and has stated it almost in the same 
way. 



LAWS OF THOUGHT. 81 

ence, but to teach them is beside our purpose ; — we 
present you only with a small specimen or tw^o for 
curiosity's sake." This course is to us unintelligible. 
The rules in question claim to be those which regu- 
late the act of reasoning ; if a system professes to 
teach reasoning, it should either give us the rules 
complete, or prove that they are false or defective. 
A large book on Logic that refers us to another book 
for the rules of the great logical act, does not fulfil 
its duty ; and suggests a suspicion that these rules 
have not been made use of as the instrument of 
scientific research — that proper trouble has not been 
taken to ascertain how far they are really applicable 
to such a purpose, and how far absurd and useless. 
I believe that if a set of rules, as free from techni- 
calities of form and expression as is consistent with 
complete accuracy, be sedulously applied to the ex- 
amination of the books we read, more especially to 
the history and theory of some particular science, 
the mind will receive great and signal benefit, and 
the creative powers will be increased as well as 
the judgment strengthened. In past days it was 
worth while to learn the scholastic terminology, be- 
cause it ran through all scientific practice ; the 
theology and metaphysics of Aquinas and Occham 
vindicate their right to spend time upon the barbar- 
isms of their Logic. Let us get by degrees a Logic 
which is to our philosophy what that of the School- 
men was to theirs, and no one will complain that 
some of its expressions are technical and its rules 
hard to understand. Technicalities are only weari- 
some, where we have no hope of their after-fruits to 
lure us through them. 



82 OUTLINE OF THE 

On these grounds, we tiy to make the analysis of 
thinking as complete as possible, and beg the student 
to master a few new names, expecting that the 
trouble so bestowed will not be grudged as a prep- 
aration for that habitual examination of thoughts 
and arguments which is the great means of teaching 
us to reason. For, the rules of Logic, those of syl- 
logism, for example, do not teach a new trick of 
argument, nor furnish an instrument by the posses- 
sion of which we are at once enabled to speak or 
dispute. There is neither trick nor magic in them ; 
they are principles which we call into use every 
hour of om* lives. They do not impart any new 
faculty, but lay bare before us the nature of that 
reasoning which has been from childhood our delight 
and our prerogative. Who shall say that this is a 
frivolous or unworthy study? 

§ 39. But it is thought advisable that young men 
who are not inclined to examine with habitual 
patience their own thoughts or the procedure in iany 
of the real sciences, should acquire some slight 
knowledge of Logic. In this case, we cannot ex- 
pect the same diligence in learning technical terms 
and rules, as they will not be required hereafter. 
But what is the course adopted ? We attenuate 
the science, where we ought to simplify it ; w^e re- 
duce the size of our manuals, in the vain hope of 
lessening their difficulty; and there remains little 
more than a catalogue of hard terms with harder 
explanations — little else than a reliquary of the di-y 
bones of that system of knowledge which five hun- 
dred years ago was alive and breathing. No won- 
der that untrained minds are repelled. Instead of 



LAWS OF THOUGHT. 83 

explanation and illustration of common things, they 
find the plainest and simplest veiled behind the 
terms of a forgotten metaphysical system ; they are 
commanded to master all the rules required for an 
extensive practice of logic, though they never mean 
to enter upon such a course, and are not encouraged 
to do so now, except by the most puerile examples. 
It is not worth their while to learn the language of 
a region of philosophy in which they are never to 
travel. Surely it would be possible to give them 
some sound and accurate instruction in the nature 
of their thoughts and minds, making use only of the 
language of common life. There are not wanting 
to our literature popular works on mental science, 
and on the intellectual processes involved in the 
physical sciences, out of which a general yet not 
inexact knowledge of the laws of mind may be 
easily acquired. 

§ 40. In the division of the subject, I see no cause 
to deviate materially from the ordinary distribution 
into three parts, the first treating of Conception, or 
the power of forming general notions ; the second 
of Judgment, or the power of deciding whether two 
notions agree or not ; and the third of Syllogism, or 
the power of drawing one judgment from -another.* 
To these a fourth part, in which Method, or the 
power of using the other three functions in the dis- 
covery of truth, is explained, has been usually added; 
which answers to the applied Logic of the present 
work. But it is proper to notice one or two objec- 
tions to this division. 

*= Another division has been adopted firom Porphyry [hag. i. 1.) 
by some logicians, who consider Logic as the science of defining, 
dividing, and arguing. 



84 OUTLINE OF THE 

§ 41. In beginning with conceptions, we arti 
charged with putting the last first. Men cannot 
get a clear conception without passing a judgment 
about it; nor can they always pass a judgment 
without certain reasonings, or syllogisms ; so that 
we go to the third part of Logic to establish what 
belongs to the second, in order that from that we 
may more clearly understand something which 
relates to the first. Why not begin then with the 
third? 

Whilst this regressive order is certainly natural, 
and whilst a Logic might be written which set out 
from the sentence or the syllogism, and analyzed it 
into judgments, and these again into conceptions, 
the contrary procedure, from the simplest element 
of reasoning, the conception, to the syllogism which 
is its complete act, will be found in our opinion 
easier to follow. The analysis has long since been 
performed, and we find it convenient to proceed by 
synthesis, in this as in many other sciences. But 
the objection is valuable, as bringing out the con- 
trast between the natural course of reasoning and 
its technical explanation. Why do we reason ? To 
find ■v\'-hether some judgment, which has suggested 
itself to our minds, be true or not. Why do we 
seek to make this judgment? To add something 
to the clearness of the notion that is its subject. 
Copernicus reasoned to prove that the globe re- 
volved round the sun ; and he established this judg- 
ment that when men thought of " the globe " in 
future they might know it as " the revolving globe." 
All the reasonings in Aristotle's Ethics are to give 
a more adequate notion of happiness, — of Plato's 



LAWS OF THOUGHT. 85 

Kepublicj to improve our notion of justice, — of 
Bacon's Organon, to afford a more accurate concep- 
tion of Method. 

§ 42. Another objection against the division is 
that it distinguishes parts which are really con- 
fused ; * that, for example, when we divide such a 
conception as that of " gases " into inflammable and 
non-inflammable, we really pass a judgment, though 
we explain division in the first part of Logic, which 
treats of Conception. 

The answer to this may be suggested by that to 
the preceding one. We do not deny that the pro- 
cesses of the mind run into one another, that a man 
judges when he forms conceptions, and so on ; we 
only ask for leave to describe each process separately. 
Our arrangement is confessedly artificial. 

§ 43. Some logicians indeed argue that properly 
speaking Judgment is no distinct act of thought, but 
rather a part and condition of every act. Every no- 
tion seems to imply a judgment ; when I think of the 
Queen, gravitation, or virtue, I mean that the Queen 
— gravitation — virtue exists ; so that we have one 
common attribute which we affirm of every thing, that 
of existence. But it is one thing to say that a judg- 
ment may be, and another that it u, made. Before 
the component parts of any complex notion could 
be brought together in the mind, many judgments 
must have been passed ; but when the notion recurs, 
we do not surely pass the j udgment over again. My 
notion of freedom implies that it is the state of being 
able to do as I will, having respect however to the 
rights of others, and that this is a state possible for 
* Damiron, Logiqiie, p. 4. 



86 OUTLINE OF THE 

men ; but I do not formally affirm either that it con- 
tains these attributes or that it is possible, and there- 
fore my mentioning freedom involves no judgment, 
although I may if I please form judgments about it 
We must carefully distinguish between a possible 
and an actual judgment — between a notion which is 
and one which may be the subject of a judgment. 

§ 44. Method, which is usually described as the 
fourth part of Logic, is rather a complete practica^ 
Logic. Whilst the other three parts describe each a 
distinct and complete product of thought, the Con- 
ception, the Judgment, and the Syllogism, no such 
whole is treated of in the doctrine of Method ; which 
may be used for making a whole science, or a whole 
speech, a system or a sentence. Method is rather a 
power or spirit of the intellect, pervading all that it 
does, than its tangible product.* Hence we put in 
the place of rules for Method as a part of Logic, an 
Applied Logic, which shows under what conditions 
in the several regions of inquiry the three acts of 
thought may be safely performed, and how far rules 
can avail to direct the mind in the use of them to 
profitable or beautiful results. 

§ 45. The attempt to apply the rules of Logic wdll 
both raise and lower the opinion which obtains con- 
cerning the worth of the science. Those who con- 
demn it altogether, as arbitrary and artificial, as a 
set of rules for arguing, put together in an age when 
truth was less the object of desire than argument, 
may find to their surprise that it is only a searching 
and systematic account of processes w^hich they daily 
perform, whether in thought, or in argument, in the 

* See the fragment on Method in Coleridge's Friend, ■vol. iii. 



LAWS OF THOUGHT. 87 

pursuit of a science or in the transactions of the stxeet 
and market. Those on the other hand who expect 
that Logic will be to them a golden key to unlock 
the treasure-house of the knowledge of the universe, 
will find that it neither gives them nor pretends to 
give, any new power ; that it only refines and 
strengthens powers they already possess ; that out 
of a dunce it never yet made a philosopher. Whilst 
its rules apply to every science, and it may therefore 
lay some claim to its ancient titles, — the Art of Arts, 
the Instrument of Instruments, — it only assists us 
in the study of the sciences, not stands in their stead. 
We must fight our own way over every inch of 
ground in the field ; but Logic will often prevent our 
throwing away our blows. She can do no more. 
Sophists of Greece may offer to teach us " a trick 
worth a hundred minae," which is to be the secret of 
all wisdom ; or Lully and Bruno may pretend so to 
arrange in tables the results of human research that 
a child may know where to put his hand on the most 
recondite secrets, and employ them at pleasure. But 
these are wild dreams of the infants of scienee, which 
thinkers in their sober, waking moments hardly men- 
tion but with a smile. We only affirm, that when 
men think, these are the rules according to which 
their thoughts run, that the knowledge of laws and 
principles, independent of ulterior profit, is always 
gratifying to active minds, and that, inasmuch as the 
clear understanding of what is right is always useful 
for the avoidance of what is wrong, Logic is an use- 
ful instrument in thinking. But it gives us the forms 
of knowledge, not the matter. It will not lay bare 
the hidden springs of moral action ; nor explain the 



88 OUTLINE OF THE LAWS OF THOUGHT. 

mystery of life, of sleep, of fancy, of memory ; nor 
display the future destination of man and the world. 
Still less will it be to us instead of eyes, if, turning 
away from this ball of earth on which we stand, we 
try to look off to the Infinite — the Absolute — the 
Eternal, whose nature will not take the mould of our 
intellectual forms, who comprehends us, when we 
vainly think that we comprehend Him. 



OUTLINE 



LAWS OF THOUGHT. 



PART I. 

CONCEPTIONS. 

"Hen obetant has discipliiwe per eas euntibus, sed circa illas hserontibus. " 

QUINOTUJA*. 



CONCEPTIONS. 




vtf- 



§ 46. Cognitions in General. 

HE impression which any object makes 
upon the mind may be called a Presenta- 
tion. Some Presentations are admitted 
into the mind without being noticed, as 
is the case with the words spoken to a dreamy or 
absent man, or with a house or tree which, form- 
ing part of a great landscape, escapes the special 
notice of the beholder. The mind is unconscious of 
them ; it sees or hears, but does not know that it 
sees or hears, so that the impression is not clear. 
And yet it is a real impression, because, when atten- 
tion is directed to it, we know that it must have 
been there before. A man stares his friend in the 
face without recognizing him ; when his friend 
awakens his attention, the recognition takes place. 
But he knows that it is not the impression upon his 
eye which begins at that point of time, but his 
attention to the impression. Presentations then are 
divided into Clear and Obscure, and the former, 
with which alone Logic is concerned, may be called 
Notions or Cognitions. 

Clear Presentations, or Cognitions, are subdivided 



92 OUTLINE OF THE 

into confused and distinct. Where the marks or 
attributes which make up the Presentation cannot 
be distinguished, it is confused ; where they can be 
distinguished and enumerated, it is distinct. For ex- 
ample, we have a clear notion of the colour red ; but 
we cannot tell by what marks we identify it; we 
could not describe it intelligibly to another; and 
hence our cognition of it is confused : again we have 
a clear notion of house ; but we can declare its 
various marks, namely, that it is an enclosed and 
covered building fit for habitation ; and therefore our 
notion is distinct. 

We subdivide the class of distinct notions twice, 
according to two principles of division ; and first, into 
adequate and inadequate notions. Adequate notions 
are those in which, besides enumerating the marks, 
we can explain them ; that is, can enumerate the 
marks of the marks of the distinct notion, and again 
the marks of those marks. As this kind of analysis 
is almost interminable, we call a notion adequate, 
not when the enumeration of subordinate marks has 
been carried to the farthest, but when they have 
been enumerated sufficiently for our present purpose, 
in whatever subject we are employed. Our notion 
of happiness, for instance (according to Aristotle), is 
adequate, when we not only know that it is " an 
energy of the soul according to the best virtue, in a 
complete life," but can explain what we mean by an 
energy of the soul, the best virtue, and a complete life. 
So we have an adequate notion of what Hobbes 
means by Right, when we not only know that it is 
" unresistible might in a state of nature," but can 
explain what unresistible might and state of nature 



LAWS OF THOUGHT. 93 

are. The same two notions would be inadequate, if 
we had the respective definitions of them but could 
not explain them. 

The other division of distinct notions is into sym- 
bolical and notative ; it has been already explained * 

TABLE OF NOTIONS. 

5C Confused. f 
... J ^ J Adequate 

ear(_ ogni lonsj -^ < i Inadequate 

Obscure. (.Distinct •< ^ 

\ Symbolical 
j Notative. 






§ 47. Intuitions and Conceptions. 

The notions formed in the mind from things offered 
! D it, are either of single objects, as of " this pain, 
that man, Westminster Abbey ; " or of many objects 
gathered into one, as " pain, man, abbey." Notions 
of single objects are called Intuitions, as being such 
as the mind receives when it simply attends to or 

* P. 45, seq. Throughout this section vre have followed Leibnitz, 
with some slight alterations. See Erdmann's Leibnitz, p. 79. Acta 
Erudit. an. 1684. Some useful distinctions in the various names of 
notions are given by S. T. Coleridge. 

" The most general term {genus summum) belonging to the specu 
lative intellect, as distinguished from acts of the will, is Representa- 
tion, or (still better) Presentation. 

"A conscious Presentation, if it refers exclusively to the subject, 
as a modification of his own state of being, is=Sensation. 

" The same, if it refers to an object, is=Perception. 

"A Perception immediate and individual, is=an Intuition. 

" The same Mediate, and by means of a character or mark com 
mon to several things, is=a Conception. 

"A Conception, extrinsic and sensuous, is=a Fact or a Cognition. 

" The same purely mental and abstracted from the forms of the 
vmderstanding itself is=a Notion." — Church ard State, p. 301. 



94 OUTLINE OF THE 

inspects [intuetur) the object. They are also called 
Singular Representations. Notions formed from 
several objects are called Conceptions, as being pro- 
duced by the power which the mind possesses of 
taking several things together (concipere, i. e. capere 
hoc cum illo) according to the principle to be ex- 
plained presently. They are also called General 
Notions or Representations. 

§ 48. Formation of Conceptions. 

On a first inspection of an object of an entirely 
novel kind, we are unable to distinguish between its 
essential and accidental properties, between what it 
must always exhibit and what it might dispense with. 
A person who had lived all his life on the shore 
of the Atlantic, would believe, unless otherwise in- 
formed, that every other sea resembled this in all 
particulars, in its tidal movement, though the Medi- 
terranean is almost tideless, in its degree of saltness, 
though the taste of the Dead Sea is much more 
bitter and its composition different, and so on. In 
travelling, or in reading a book of travels, he is made 
acquainted with another sea with properties not 
quite identical indeed, but still so far similar that 
he cannot help regarding the new specimen as of 
the same kind as the old. This he sees at once 
upon making the comparison of the two objects ; 
and he then proceeds to reflect upon the properties 
of each, with a view to discover the points in which 
they agree, as well as those in which they are at 
variance. Having ascertained what they are, he sees 
that a separation must be made between the dis* 



LAWS OF THOUGHT. 95 

pensable and the indispensable properties, because 
the latter will belong to each and every specimen of 
this kind, whilst the former, as he now sees, need 
not be present to constitute a sea what it is. He 
proceeds then to abstract, or draw off (abstrahere), 
the points in which seas are to agree from those in 
which they may differ ; and the properties so drawn 
off and kept apart, are called the Notes or Marks or 
Attributes of a sea, and form when taken together a 
Universal or Common Nature ( Universale). But he 
cannot think of a common nature without implying 
a class of things, be the number large or small, in 
each of which this set of attributes is to be found, 
and each of which must exhibit them as its creden- 
tials for admission into the class ; in taking this fur- 
ther step he generalizes, or forms a Genus or Class. 
Lastly, as he cannot be sure of remembering the 
class, nor hope to recall it to the minds of others 
who have gone through, or who at least take for 
granted, the same steps of thought, without a name 
to represent it, he either invents a new name, or ap- 
plies that by w^hich he once designated a single 
thing, to the whole class ; which is an act of 
Denomination. 

There are here no less than five steps, which must 
have b€en taken by every one who fully and fairly 
realizes a general notion, and some of which must 
have been made even by those who have a less dis- 
tinct apprehension of what they mean when they 
speak of classes, i. Comparison is the act of putting 
together tw^o or more single objects with a view to 
ascertain how far they resemble each other, ii. Re- 
flection is ascertainment of their points of resem- 



96 OUTLINE OF THE 

blance and their points of difference, iii. Abstrac- 
tion is the separation of the points of agreement 
from those of difference, that they may constitute a 
new nature, different from, yet including, the single 
objects, iv. Generalization is the recognition of a 
class of things, each of which is found to possess the 
abstracted marks, v. Denomination is the imposi- 
tion of a name that shall serve to recall equally the 
Genus or Class, and the Common Nature. 

The process thus analyzed into five acts is often 
described generally by the principal of them, as Ab- 
straction ; and for convenience' sake that word shall 
be reckoned sufficient here. 



§ 49. Higher and Lower Conceptions. 

The functions of Abstraction do not cease, as soon 
as we have compared several intuitions, to form one 
conception. We may proceed to form a larger con- 
ception from several narrower ones ; and this too is 
done by Abstraction. By observing John, Thomas, 
and Peter, and abstracting from their accidents the 
essential marks, we get the notion of man ; but again, 
by comparing the conception man with other con- 
ceptions, cow, sheep, wolf, whale, and observing the 
mark common to all, that they suckle their young, 
we form the wider conception Mammalia, — wider, 
because it concludes man and many other concep- 
tions. We may carry the process farther still ; and, 
with writers on Natural History, compare the Mam- 
malia, with Aves, Amphibia, Pisces, Insect®, and 
Vermes, when we shall discover that all these, how- 
ever different, agree in having life and sensation, from 



LAWS OF THOUGHT. 97 

which marks we gain the new conception animal, 
wider than any of the former, as including them all, 
— higher, as requiring a second step in the abstrac- 
tive process to reach it. 

§ 50. Genus, Species, Individual. 

In this scale, composed of more or fewer steps, the 
lowest is always the intuition or Individual. The 
next is called the Lowest Species {infima species), 
which can only contain single objects, not subordi- 
nate kinds or classes. AH the higher rounds of the 
ladder, except the highest, are called Subaltern [sub- 
alterna) Genera, which are alternately genera and 
species, genera to the lower, and species to the higher 
and wider conceptions'. The widest class, with which 
Abstraction ceases, is called the Highest (summum) 
Genus, because in this hierarchy of conceptions it is 
not brought under any other genus as its species, but 
is itself the genus to each conception in the series. 
Thus the 

Individual is neither genus nor species. 

Infima Species is never a genus. 

Summum Genus is never a species. 

Subalterna Genera are genera to those below them, 
and species to those above.* 

A series of this kind, in which the same individuals 
are found throughout, is called a system of cognate 
genera. Thus, in the series Socrates, Philosopher, 
Man, Animal, the same individual, Socrates, is found 

* With the Greek Logicians the Summum Genus is jevog yeviKura- 
Tov, the Infima Species, eliog eldiKUTarov, the subaltern genus, elSoj 
uiaov mi vixoKKriKov. 

7 



98 OUTLINE OF THE 

in each of the three conceptions, and might have the 
name of it applied to him. 

It must be remarked that the Suramum Genus 
and the Infima Species are fixed somewhat arbitrarily. 
There can only be one absolute summum genus, and 
we may go on abstracting until we come to some 
wide notion, be it " thing " or " substance " or " es- 
sence " or " object," that comprehends all that we 
can think about. If we stop short of this, as the 
Naturalist does when he makes Animal his highest 
genus, the name can only be used in a qualified 
sense, and our genus is only the highest because we 
will make it so. Then, we can scarcely ever ascer- 
tain the infima species^ or that kind that is too nar- 
row to be divided into other kinds, because even in 
a handful of individuals we cannot say with cer- 
tainty that there are no distinctions upon which a 
further subdivision into classes might be founded. 

The genus next above a given species is called 
proximate ; those that are still higher are called re- 
mote. A number of species that have the same 
proximate genus are said to be coordinate. 

§ 51. Marks or Attributes. 

Those properties by which we recognize any ob- 
ject, and assign it a place under some appropriate 
conception, are called its marks. K these are inva- 
riably found in the objects of a given sort, they are 
called essential ; if only a portion of the class pos- 
sesses them, they are accidental. The whole of the 
essential marks of a species make up its specific 
character, or its essence. Two marks which are in 



LAWS OF THOUGHT. 99 

the very mode of expressing them opposed to each 
other, as wise and unwise, mortal and immortal, are 
called contradictory, because it is impossible to assign 
them to the same object without a contradiction in 
terms ; and this is certain a priori, because the one 
is the mere negation of the other, so that their oppo- 
sition does not depend on an examination into the 
nature of these marks. If they were represented as 
A and not- A, we should be as sure that they were 
diametrically opposed, as if A was a word of well- 
known meaning, instead of an arbitrary symbol. 
Marks which are opposed to each other, but not as a 
positive and negative, so that we know their contra- 
riety a posteriori., from experience, as sweet and sour, 
hard and fluid, are termed repugnant marks. Those 
which may meet in the same object, as sweet and 
fluid, sour and hard, we may call compatible. 

§ 52. Extension and Intension. 

When we compare a vague and general concep- 
tion with a narrower and more definite one, we find 
that the former contains far more objects in it than 
the latter. Comparing plant with geranium, for ex- 
ample, we see that plant includes ten thousand times 
more objects, since the oak, and fir, and lichen, and 
rose, and countless others, including geranium itself, 
are implied in it. This capacity of a conception we 
call its extension. The extension of plant is greater 
than that of geranium, because it includes more 
objects.* 

* Mr. Mill, Logic, i. vii. 1, thinks it only " accidental " that " gen 
eral names " should be the names of classes. But his own language 
contradicts him ; if they are general they belong to genera ; it cannot 
be accidental that a class-name should be the name of a class. 



XOO OUTLINE OF THE 



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LAWS OF THOUGHT. 101 

But conr-eptions have another capacity. Whilst 
plant has more objects under it than geranium, it 
has fewer marks in it. I can describe the leaves, 
petals, stamina, and pistils of geranium ; but of plant 
no such description is possible. I cannot say that 
every plant has a stem, for there are the lichens to 
contradict me ; nor a flower, for ferns have none, 
and so on. I can say little more about plant, than 
that all plants have growth and vegetable life. The 
logical expression of this defect is, that its intension 
is very limited. 

The greater the extension, the less the intension ; 
the more objects a conception embraces, the more 
slender the knowledge which it conveys of any of 
those objects ; and vice versd* 

With the help of the important distinction between 
extension and intension, or, as others express it, the 
sphere and matter of the conception, magnitudo et 
vis conceptus, we can understand the meaning of 
the saying — that the subject of a judgment is in the 
predicate, and the predicate in the subject. " Man 
is an animal ; " this conveys two notions, that man 
is contained in animal, as a species in a genus ; 
and that whatever makes up our notion of animal 

"^ The various modes of expressing the double capacity of concep- 
tions are as follows : — 

A conception viewed as a 



Logical whole 


Metaphysical whole 


has 


has 


Extension 


Intension or Comprehension 


Breadth 


Depth 


Sphere 


Matter 


Objects 


Marks 


Power to denote 


Power to connote. 



102 OUTLINE OF THE 

—all the marks ot animal — are contained in (vnapxeL*) 
man. So they are mutually contained. 

§ 53. Determination. 

The reverse of the abstractive process, that of 
descending from higher conceptions to lower, by re- 
suming the marks laid aside, is called determination. 
Thus from the broad class of diseases, we determine 
or mark out the class of fevers, by the peculiar symp- 
toms of heat, rapid pulse, &c. which are their marks ; 
and from fevers we descend further to intermittent 
fevers, by bringing in the fresh mark of time. 

As abstraction augments the extension by dimin- 
ishing the marks, so determination augments the 
intension by increasing them. Notions of individu- 
als, and they only, are said to be fully determined, 
because to them there are no more marks to add. 
The use of the word determination in its logical 
sense is already sanctioned by our older writers. 

§ 54. The three powers of a Conception. 

That all simple cognitions have three powers or a 
threefold value, in that they consist of marks, and 
include objects, and are summed up in names, has 
been stated already. To these three functions as 
many processes correspond ; Division of a Concep- 
tion enumerates all the objects or classes that are 
included under it, and so deals with the extent of 

* Aristotle (Anal. Pri. I. i., and many other places) adopts in 
preference this mode of putting the proposition. Instead of " Man 
is an animal," he has " Animal inheres in man." 



LAWS OF THOUGHT. 103 

the notion; Definition expounds all the marks im- 
plied in the notion, and so represents to us the nature 
or specific character of it ; and Denomination, and 
Explanation of Names, affix the verbal sign to a 
conception, and interpret given verbal signs already 
in use, so that they may be referred to the notions 
they really represent, and to no others. The nature 
of these processes must be explained more in detail. 

§ 55. Logical Division. 

Division is the enumeration of the various co- 
ordinate species of which a proximate genus is 
composed. The rules for conducting this process 
correctly are 

i. The constituent species, called the dividing 
members [membra dividentia), must exclude one 
another. 

ii. The constituent species must be equal, to- 
gether, to the genus divided (diviSum). 

iii. The division must be made according to one 
principle or ground [fundamentum divisionis). 

The reason of these rules, and of the terms of the 
explanation of Division, will be apparent when the 
uses to which the process was intended to minister 
are fairly considered, and these, although they be- 
long rather to applied Logic, may be introduced 
here. The treatment of a subject is greatly facili- 
tated by an orderly arrangement of its several parts. 
If Natural History, for example, were to go no 
further than its name seems to require, if it were a 
mere collection of curious information about natural 
products, without order and completeness, no mem^ 



104 OUTLINE OF THE 

ory would be able to master its details. Omissions 
would detract from its value ; and repetitions would 
disgust the student. But it maps out the kingdom 
of nature into great districts, and subdivides these 
into smaller portions, so as to secure us from serious 
omissions, to preclude confusion, and to assist the 
memory ; and so becomes worthy of the name of a 
science. The first rule then, as given above, is to 
secure that the classes and subclasses shall be dis- 
tinct from each other, that they shall not overlap 
each other, or be what Leibnitz calls communicant 
species. Exceptions to this rule are often unavoid- 
able, especially in subjects that do not belong to 
strict science ; thus, in enumerating the species of 
imaginative writers, one would probably mention 
poets, dramatists, and writers of tales ; yet some 
poets are dramatists, and some tales are poems. 
The second rule provides that no class shall be 
omitted, and secures completeness. The principle 
of division mentioned in the third rule is some new 
conception, for the marks of which we seek in the 
conception to be divided. Thus man may be divid- 
ed into European, African, Asiatic, American, and 
Australian ; and again into Christian, Mohammedan, 
Jew, and Pagan, and again into just and unjnst; 
and in the first division locality, in the second relig- 
ion, and in the third behaviour, is the principle of 
division * Now as it is impossible to divide without 

* Where we divide a conception upon several principles, tbe whole 
number of the dividing members will be the product of the numbers 
under the several principles multiplied together. In the example in 
the text, the principle of locaUty gives 5 species, religion 4, and be- 
haviour 2 ; then the whole number will be 5 X 4 X 2 = 40. For 
Europeans may be subdivided into 4 classes according to their relig- 



LAWS OF THOUGHT. 105 

seeking for marks of difference, and as the enume- 
ration of marks is the explanation of the nature of 
an object possessing them, it is plain that no Divis- 
ion can take place without unfolding some of the 
properties of the conception divided. It is true that 
trifling and useless divisions, like those in the 
Sophist of Plato (which perhaps were not intended 
to be regarded seriously.) have brought the process 
into some contempt ; but in many sciences a natural 
division, or one which is based upon natural proper- 
ties, and not upon fancies or trifling resemblances, 
is of great use both in arrangement and in securing 
a full and complete knowledge of a subject. Thus 
in that branch of medicine called Materia Medica, 
where the mode of treatment is purely divisive, it 
will be found that almost all the various schemes by 
which drjigs are classified involve so many distinct 
theories of medicine. 

But as we descend from a high genus to a species, 
we must avoid a sudden leap ovet any of the sub- 
altern genera in the series (divisio nonfaciat saltum), 
because their distinctive properties may be over- 
looked at the same time ; and henpe division was 
described above as the enumeration of the species 
of the proximate genus. Subdivision is the process 
of dividing some species of a genus already sub- 
jected to that operation ; and it may be repeated 

ion, and so may each of the rest ; then each of the subdivisions may 
be again divided according to uprightness of conduct ; so tliat we 
have European- Jews who are just — Asiatic-Jews who are just, and 
BO on, up to 40 combinations. This logical subtlety is of little prac- 
tical importance, because, amongst other reasons, many of the subdi- 
visions will commonly be entirely vacant. See Drohisch. Logik, \ 
119. 



106 OUTLINE OF THE 

until we reach the lowest species, which we cannot 
properly divide, though the individuals contained 
under it may be enumerated. A division where the 
species are not coordinate, although correct in other 
respects, would offer a bad arrangement for pur- 
poses of science ; thus. Sciences should not be di- 
vided by a reader of Aristotle into " Theoretical and 
practical, together with Poetry, Rhetoric, and Dia- 
lectic," because the first two are divisions, and the 
last three are subdivisions of a genus that has been 
omitted, namely, the Poetic Sciences. 
'^' Logicians test every division by the possibility of 
reducing the constituents to two, a positive and a 
privative conceptiono If A is a genus divisible into 
the species x, y, and z, we may represent the dividing 
members as x and not-x, the latter being really equiv- 
alent to y and z. This division into two members 
{divisio debet esse bimembris) called dichotomy ((5^'°- 
Toiiia) is alone purely logical, because we know a pri- 
ori, and without any researches into the particular 
case, that it must be complete. But on the other 
hand it is comparatively useless,* because, of one of 
our constituents, and that the larger, we know noth- 
ing but that it wants the marks of the other. " In- 
sincerity," so long as it remains in our mind as a 
merely privative conception, implies nothing, except 
that it has not the mark or marks that sincerity has. 
The mind, however, does not allow conceptions to 

* Compare the mode of stating this objection in Plato, Politicus, 
262, C. D. Toiovds olov . . . tuv axiod-evruv. If, as Rassow and Wailz 
suppose, Aristotle had Plato in his mind in censm-ing the divisive 
method, as useless in the discovery of truth (see An. Post. II. ch. 5, 
and An, Pri. I. ch. 31), we believe that Plato saw its defects per 
fectly. 



LAWS OF THOUGHT. 107 

retain their merely privative character ; such words 
as infinite, intolerant, undying, become substantial 
conceptions, as much so as those with which they are 
contrasted by the form of their expression. 



§ 56. Partition. 

The separation of the parts of any individual ob- 
ject, as of a sword into blade and hilt, is termed 
partition. An individual (aro/io ) is that which can- 
not be divided without ceasing to be what it is ; its 
parts cannot have the name of the whole. When 
a genus is divided, every part of it remains un- 
changed, and may have the name of the genus. 
The trunk and limbs of a man cannot be severally 
called the man ; but a European is a man, and so is 
an Asiatic and an American. 

§ 57. Definition of a Conception. 

As Division ascertains the various classes of ob- 
jects united under one Conception, so does Defini- 
tion ascertain those common marks which all the 
objects possess, or that common nature represented 
by the conception. Division therefore answers to 
Generalization (§ 48), and Definition to Abstraction; 
the former viewing the conception only as a class, 
the latter only as an abstract nature or set of proper- 
ties. The attributes of this nature may none of 
them be peculiar to it when taken singly, provided 
that the whole of them do not concur in any other 
conception. Hence every definition will recount the 
marks of the genera above the conception it has to 



108 OUTLINE OF THE 

unfold, together with some other mark called the 
Difference, by which this species is distinguished 
from every other. But this difference may only be 
a distinctive mark when brought into its present 
connection ; apart from which it may be an attri- 
bute of some high and wide genus. 

As Definition and Division are but two sides from 
which the same conception is viewed, they might be 
expected to lend each other assistance. (§ 52.) In 
dividing successively a set of cognate conceptions, 
from the highest to the lowest, we do in fact bring 
in one by one the marks that compose the definition, 
and hence the fullest and most complete definition 
would be formed after such a process of division had 
been gone through, provided, of course, that essen- 
tial marks, and not mere accidental ones, had been 
brought in to divide by. Definition in turn, by 
enumerating the essential marks of a conception, 
furnishes a guide to its genus, and its coordinate 
species ; thus if " animal " were defined " an organ- 
ized being with life and sensation," its proximate 
genus would appear to be that of " organized living 
beings," divisible into those which had and those 
which were destitute of sensation. 

The rules of Definition may be stated here, as a 
help to understanding the process itself, although 
they belong more properly to applied Logic. 

1. A definition must recount the essential attri- 
butes of the thing defined [Definitlo fiat per notas 
rei essentiales). Thus, in defining "words " as " the 
articulate signs of thoughts," we are not to introduce 
such a superfluous mark as " Words are the articu* 
late signs by which an orator expresses his thoughis,' 



LAWS OF THOUGHT. 109 

for whilst this is true, it is not necessarily found in 
the conception in our mind, and consequently has no 
place in the act of analyzing it. 

2. The definition must not contain the name of 
the thing defined ; as this is precisely the word we 
are bound to explain. Thus if " life " is" defined to 
be "the sum of the vital functions," we have not 
logically defined " life," as the word " vital," which 
implies life, stands unexplained in the definition. 
This fault is called circulus in definiendo (also dml- 
a?;Aof rpoTTOf), because vital is given to explain life, and 
life would be used probably to explain vital, so that 
we should travel " in a circle " back to our old dif- 

■ ficulty. 

3. A definition must be precisely adequate to the 
species defined [Definitio sit adcequata, neque latior 
neque angustior suo definito). If it explains a spe- 
cies below, it is said to be too narrow, as when 
triangle is defined " a rectilinear figure with three 
equal sides and angles," If it is applicable to the 
genus above, it is too wide, as when we define words 
as " the signs of thoughts," whereas there are other 
signs also. 

4. A definition must not be expressed in obscure 
or figurative or ambiguous language. Oken's defi- 
nition of Phild'sophy cannot avail much ; it is "the 
recognition of mathematical ideas as constituting the 
world." The Divine Nature has been represented as 
" a circle whose centre is everywhere, and whose cir- 
cumference is nowhere;" but this bold figure cannot 
for a moment be accounted a definition. 

5. A definition must not be negative, where it can 
be afi[irmative. " Evil is that which is not good. A 



110 OUTLINE OF THE 

point is that which has no parts and no magnitude." 
These definitions are to be judged according to our 
view of the possibility of finding others of the affirm- 
ative form. Some conceptions are in their nature 
negative, as indivisibility, blindness, and must be de- 
fined negatively. 

The position which definition holds in the construc- 
tion of a science need not be discussed here ; it be- 
longs to the appKcation of Logic. 

§ 58. Third power of Conceptions. Denomination. 

A Conception is not complete until it has received 
a name, to preserve and represent it for the future 
(p. 52). The principal divisions of nouns or names 
are the following. 

a. Nouns are either Proper, Singular, or Common. 
A proper name represents a single object, apart from 
that connection with others, which is effected in ab- 
straction (p. 95), as Socrates, Rome, Sirius. A com- 
mon noun applies to a class of objects, and their 
common marks or attributes, ascertained by abstrac- 
tion, as man, city, star ; and it applies to each and 
every one of the objects in that class. A singular 
noun applies to only one object, like a proper name, 
but then it is only singular in its present application, 
as, a song, this world, my horse, the King of Prussia; 
it is evident that song, world, horse, king, are com- 
mon nouns, and their singular meaning is obtained 
by adding some word of limitation. 

b. Distributive and Collective Nouns are to be 
distinguished. The former are common nouns, the 
latter nouns of multitude ; the former are applicable 



LAWS OF THOUGHT. Ill 

to each and every one of the objects they denote, the 
latter, though demoting many objects, can only be 
applied to them when combined, as army, senate. 
Sometimes it is important to distinguish between the 
distributive and collective uses of words that may 
assume either form ; thus, " All that glitters is not 
gold," means " all taken together," not " each and 
every thing ; " and " the Greeks conquered the Per- 
sians," means " the Greeks as a body," whereas " the 
Greeks loved philosophy," means " each Greek." 

c. Nouns are either Substantives, Attributives, or 
Relatives. Substantives are names of things, which 
have either in fact or in thought an independent 
existence, as Charlemagne, botany, wisdom. Attrib- 
utives are nouns which assign a mark to a substan- 
tive, as great, good, docile. Relatives are pairs of 
nouns, each of which implies the existence of the 
other, as father and son, debtor and creditor, king 
and subjects. The properties of relative conceptions 
must be further explained below. 

d. Nouns are either Positive, which stand for cer- 
tain definite marks and an ascertainable class of ob- 
jects, or Privative, which only imply the absence of 
certain marks, and consequently belong to a vague 
and indeterminate class. Of the former, mortal, sin- 
cere, honest, are examples ; of the latter, immortal, 
insincere, dishonest. This is a distinction of some 
importance in Logic, as will appear hereafter. 

e. Nouns are either Univocal, Equivocal, or Anal- 
ogous, in their signification. Univocal nouns have 
one meaning only, in which they are applicable to 
the objects they stand for. Equivocal have several 
meanings, and are in fact several words, with a casual 



112 OUTLINE OF THE 

resemblance in form, as gall, for a wound and a bitter 
substance ; ball, for a dance and an orb ; light, for 
the contrary of darkness and that of heavy. In anal- 
ogous nouns, one meaning is extended to new sets 
of objects from some proportion or resemblance be- 
tween them, as foot, extended from a part of an ani- 
mal to the lowest part of a tree, a mountain, and 
the like. Where equivocal or analogous words are 
to be employed in Logic, it is requisite to give them 
the power of univocals, by adding words to specify 
the exact application we mean to make of them. 
Analogous words pass into equivocals as soon as we 
lose sight of the analogy that connects them; this 
has occurred in post, and in file as applied to a string 
of papers and a line of soldiers. 

§ 59. Privative Conceptions. 

Besides conceptions which arise from marks, there 
are others formed from the privation or absence of 
marks. Our notion of kindness arises from some 
properties which a kind person always exhibits ; but 
whence our notion of its opposite, unkindness ? 
From the want of the marks, whatever they may be, 
of kindness. So, too, in marking by a name any 
class of objects, as animal or stone, we necessarily 
imply that there are corresponding classes which are 
not animals and not stones ; about which, it is true, 
we know very little, as we can only say what they 
are not. Any pair of conceptions, a positive and a 
privative, must, speaking absolutely, divide the whole 
universe. Either in man or in not-man, all objects 
must be found, — star, flower, form of government, 



LAWS OF THOUGHT. 113 

moral quality, and any other things the most unlike. 
But practically we limit this absolute division ; though 
unkind does include every thing except the beings 
that show kindness, it would be absurd to apply it to 
the whole of these. It is more convenient to think 
of such a pair of conceptions as kind and unkind, as 
dividing between them, not the whole universe, but 
some proximate genus, say man or moral being ; so 
that we mean to include in our notion of unkind not 
every thing that is unkind, but every man that is so. 
Such a larger conception, which a positive and a pri- 
vative divide between them, may be called the second 
sphere of the positive.* 

Privative conceptions not only afford the means 
of varying the forms of thinking, by furnishing for 
every affirmative judgment, equivalent negatives, and 
for every negative, affirmatives, but they enter into 
and assist the higher processes of the reason in all 
that it can know of the absolute and the infinite. To 
attribute the properties of one or many individuals to 
every other of the same class is within the reach of 
the mere understanding, and the brute creation enjoy 
some share of it ; but from the seen to realize an un- 
seen world, not by extending to the latter the prop- 
erties of the former, but by assigning it attributes 
entirely opposite, is a prerogative of reason alone. 

* The devrepa ohaia of Aristotle (Cat. Ch. v.) may justify the term 
second sphere. Professor De Morgan proposes to call it the universe of 
the positive conception. The privative has been caUed by some the 
contradictory, by otliers the contrary, of the positive ; but either ex- 
pression tends to confound conceptions with judgments. 



114 OUTLINE OF THE 



§ 60. Relative Conceptions. 

There is a class of conceptions which have the 
peculiarity that none of them can even be thought 
of alone, that the existence of each implies and de- 
pends on some other; thus a father implies offsprings , 
a king implies subjects, a debtor a creditor, and so on. 
Some of these are of distinct things or beings, like 
the examples just given ; and are expressed by nouns 
substantive ; but other relatives are only attributes, 
expressed by adjectives ; thus larger implies less^ 
akin implies a relationship to some one, near, high, 
heavy, have reference to some standard of distance, 
stature, or weight. 

A Relation is either simple or complex ; simple 
where it subsists between two correlates, as between 
debtor and creditor, complex where it is a relation of 
relations, i. e., where it binds two or more pairs of rel- 
atives together. Thus the word family implies not 
merely a set of simple relationships, between father 
and son, brothers and sisters, but the action of these 
relationships upon each other. The word state in 
like manner implies not only the aggregate of the 
relations betu^'een the several classes, but the mode 
in which these simple relations act on and modify 
one another. 

The relative conceptions that appear as adjectives, 
as great, distant, require no separate treatment. Con- 
ceptions have two kinds of marks, namely, atti'ibutes, 
which belong to the conception in itself, and rela- 
tions, which belong to it when viewed in connection 
with other conceptions. To say that man is mortal 



1.AWS OF THOUGHT. 115 

is an act of attribution, for mortality is a quality re- 
siding in himself, without any reference to other 
beings ; to say that man is long-lived, is to bring 
him into relation or comparison with other creatures 
whose days are shorter than his own. Relative ad- 
jectives then express a particular kind of marks of 
conceptions. 

Simple relations expressed by substantives, are not 
more difficult to dispose of. These relatives always 
appear in pairs, — father and son, ruler and subject ; 
and that which is the more prominent in thought at 
a given time is called the relative, and the other its 
correlative. This order however can always be in- 
verted ; if it is the property of a ruler that he has a 
subject, then inversely he is a subject that has a ruler. 
But what is it that thus connects them ? A certain 
act or state of facts, called the ground of relation 
{fundamentum 7'elationis) ; for relatio non est ens per 
se reale^ sed per suum fundamentum. Li one of our 
examples the ground of relation would be procreation 
of offspring, in the other civil government. Now if 
a pair of relatives, with the ground of their relation, 
are to be resolved into substance and attribute, as 
other conceptions are, this will be possible in three 
different ways, the facts of course remaining the 
same, and the order of thought alone varying. The 
relative may be viewed as substance, and the cor- 
relative may become its attribute, or this may be 
inverted ; or thirdly, the ground of relation may 
become the substance of which both the correlatives 
are attributes ; thus, we attribute to the ruler that he 
has subjects, or to the subjects that they must have 
a ruler, or to civil government that it implies a ruler 



116 OUTLINE OF THE 

and subjects. Nor is it necessary to break the sym 
metry of the doctrine of conceptions in order to find 
a place for what may at first appear to demand it by 
their peculiarity of form. 

§ 61. Abstract and Concrete Representations. 

Abstract and concrete are relative terms ; when a 
higher conception is seen to exist in a lower, or in 
an intuition, as we see the marks of animal in the 
conception horse or a horse, we are said to see the 
abstract in the concrete. So of two cognate con- 
ceptions, the more abstract bears the name of the 
abstract, the more fully determined we call the con- 
crete. 

The received explanation among logicians in this 
country is that an abstract term is the name of a 
quality considered apart from the subject in which 
we should look to find it, as prudence, strength ; and 
that a concrete term is a name expressing the qual- 
ity as residing in some subject, as prudent, strong. 
There is an analogy between this narrow sense, and 
that assigned by us ; we say that the abstract is to 
the concrete as universal to particular, and they, 
that it is as the general quality to particular cases 
of it.* 

§ 62. On the nature of general Notions. 

There is a pretty general agreement at present as 
to the mode of the existence of general notions ; the 

* See the excellent note in Trendelenburg. Excerpta : on § 86. 
Also Waitz on Organon. Comm. on 81, 6, 3 ; Trendelenburg on Ar.. d« 
Anima, 478. 



J 



LAWS OF THOUGHT. 117 

differences of opinion referring chiefly to the use that 
shall be made of them. Formed in the mind, they 
are not entirely dependent upon its mere arbitrary 
decision ; because in most cases there are properties 
in the objects around us which compel us to gener- 
alize in a particular way. Every nation, for exam- 
ple, would without any express convention put men 
into one class and horses into another, because the 
common properties of men are so marked and strik- 
ing, that they seem as it were to cry aloud to be 
classed together. No one would be absurd enough 
to neglect such similarities ; and to put some men 
and some horses invariably into one class, because 
they were white, and some other men and some 
other horses into one class because they were 
black ! General notions exist in the mind alone; but 
they are founded on common properties which exist 
without the mind, not in a separate state, but as 
inherent in the objects of intuition. Further, these 
common properties were given to the various objects 
by design. For example, when the same vertebral 
column is found in a hundred species of animals^ 
sometimes joined to large and powerful limbs, some- 
times to small, rudimentai ones, now to wings, now 
to fins, and now to arms, sometimes carried verti- 
cally, sometimes horizontally ; and when, amidst all 
the specific variations, many of them modifying its 
own structure, the vertebral column is easily recog- 
nized as fundamentally unchanged, it is natural to 
infer that the possession of this part of the frame 
was preordained to be the link of connection of 
these species,, and that in forming a class of " Ver 
tebrate Animals " we are seeking after a form or 



118 OUTLINE OF THE 

idea which was in the Divine jVIind when animals 
were created. So that general notions exist without 
the mind of man, in as far as they are in another 
mind. The Divine Mind stamps them on material 
things ; the human reads them there. 

With the controversies upon this question, and 
with the various opinions indicated by the names, 
Realism, Nominalism, and Conceptualism, we need 
not concern ourselves much in this place ; they must 
be studied historically, in their connection with Theo- 
logy' and in the order of their development, before 
we can hope to understand them. StUl, a few re- 
marks may be of use in guiding those who have 
time to pursue the study. 

The question concerns Universals (universalia), 
or those general properties which many things share 
alike, and which are acquired by the mind only by 
ab^acting from the things that exhibit them (§ 48). 
These Universals have names of their own, just as 
much as the most tangible things ; whiteness, hu- 
manity, animal, may serve as examples. Now the 
question, broadly stated, to the neglect of many nice 
subtleties and shades of opinion brought out in the 
history of the controversy, is this — Are these Uni- 
versals real existences, apart from the mind that has 
formed them by absti-action, and independently of 
the things in which alone they appear to us, — or are 
they mere modes of intellectual representation, that 
have no- real existence, except in our thoughts ? 
Those who adopted the former alternative were 
called Realists ; those who adhered to the latter 
might fitly be designated by a name of later origin, 
as Conceptualists, if we should object to the name 



LAWS OF THOUGHT. 119 

of Moderate Nominalists, which indeed would imply- 
that they held these Universals to be mere names. 
To each of these more moderate opinions belongs a 
cognate exaggeration ; so that there are four princi- 
pal answers to the question — what are Universals. 

1. That of the Ultra-realists. Universals, or the 
Ideas of things, are real existences, nay, inasmuch as 
visible things change, grow, decay, and perish, the 
Universals or Ideas are the only real existences, for 
they are subject to none of these conditions. Wise 
men perish ; but the idea of wisdom, of which they 
partake, after which they have their name, perishes 
not, does not change, — is the same in the Seven 
Sages as in the philosophers now living. In con- 
formity to these ideas the world was created ; and 
thus they even governed and guided the creating 
mind itself. This form of Realism has been attrib- 
uted to Plato ; but it is probable that he stopped 
short of believing that the Divine Mind was subject 
to the ideas. What general notions are to our minds 
— he probably held — ideas are to the supreme reason 
[vov^ (SaacAEvg)', they are the eternal thoughts of the 
divine Intellect, and we attain truth when our 
thoughts conform with His — when our general no- 
tions are in conformity with the ideas. It is, how- 
ever, very remarkable that Plato has left his opinions 
upon this important point open to a reasonable 
doubt* 

2. That of the Realists. Universals exist inde- 
pendent of things and of our conceptions of them, 
in the Divine Intellect. Under various forms this 
doctiine — of universalia ante rem — was the doclrine 

* Stalbaum, Prol. to Plat. Parm. p. 269. 



120 OUTLINE OF THE 

of the Schools before Roscelin, and of the Realist 
Schoolmen after him. 

3." That of the Moderate Nominalists. Universals 
exist as a product of the mind only ; they are formal 
representations of things, constructed by the mind 
through the assistance of language. Occham founded 
his Nominalism (so called) upon the position Nullum 
universale est aliqua substantia extra animwn ex- 
istens* Many shades of opinion, however, are to be 
detected among the Moderate Nominalists ; and that 
of the Conceptualists, represented by A.belard, should 
be particularly studied. 

4. That of the Ultra-Nominalists. Universals are 
mere names ; and the only realitie^are individual 
things, which we group together by the aid of names 
alone. The name of Roscelin is usually connected 
with this opinion ; but in what sense he held that 
Universals were only flatus vocis, we cannot decide 
from the scanty and adverse accounts in our posses- 
sion. 

Before we indicate some of the principal sources 
of the history of Nominalism and Realism, one re- 
mark is to be made, which, if it will not remove the 
difficulties of the subject, will perhaps define the 
common ground upon which the more moderate of 
both the adverse parties may be brought together. 
Making allowance for much confusion of statement 
in the scholastic writers, and for extreme assertions, 
which, there is reason to think, their authors under- 
stood in a modified sense, we have two views of the 
nature of general notions ; that of the Realist, who 
maintained that they exist in the mind and also with- 

* Logica, i. 15. 



LAWS OF THOUGHT. 121 

out it — in the Divine Mind ; and that of the moder- 
ate Nominalist, who held that they exist only in the 
mind as notions, and that we use names to fix and 
recall them. Now I venture to think that the inter- 
minable contest between Platonist and Aristotelian, 
Realist and Nominalist, is at bottom, not so much a 
question of what universals are, as of how they 
shall be treated ; not so much a question of Meta- 
physics, as of Method. Upon the nature of general 
notions there is a large amount of agreement be- 
tween the parties : the Realist believes, with the 
Nominalist, that they are in the human mind, whilst, 
if the Nominalist believes at all that the world was 
created by design, he can scarcely escape from recog- 
nizing the Realist's position, that such ideas as ani- 
mal, right, motion, must have had their existence 
from the beginning in the creative mind. Whence 
then the controversy? The burden of Aristotle's 
objections to the Platonic scheme of ideas is, tj^at it 
teaches what cannot be- known, and gives out as 
certain truth what lies far beyond the reach of our 
powers of investigation. " Instead of being con- 
tent," he would say to the Platonist, " with classify- 
ing particular objects so as to form general notions, 
which we could always compare with the objects, as 
being inseparable from them, you jump to certain 
ideas, separate from the objects, though they cause 
and determine the manner of their existence, fcied 
whilst these are changeable, eternal whilst these pass 
away. Be it so ; you offer these transcendent ideas 
to our understanding — you must remove the difficul- 
ties which the understanding meets in receiving them. 
How do you know that they exist ? For we must 



122 OUTLINE OF THE 

not, in order to explain the world which we sec, de- 
vise another world, of ideas, which no eye has seen.* 
Again, how they are connected with the things to 
which they belong? The man, for instance, with 
the idea of humanity ? To say that things ' partici- 
pate ' in, or ' are copies ' of, the ideas, is to avoid the 
difficulty by vague metaphorical language. Must 
there be an idea for every sensible object? If so, 
before Socrates could be born, there must have been 
an eternal idea of Socrates ; which would lead us 
to a multiplication of ideas too great even for the 
imagination. In a word, you cannot explain the 
properties of these ideas without vagueness and 
self-contradiction ; and, therefore, should not assume 
them to exist and found a system upon them."f 

If this view be correct, Aristotle does not so much 
intend to deny the existence of ideas, as to maintain 
that the evidence for them is insufficient, and that 
no s^fstem can stand secure upon so weak a founda- 
tion. And looking to the paradoxical and seemingly 
inconsistent statements of Plato on the one hand,J 
and the evident misapprehensions of Aristotle upon 

* So Occham — " Entia non sunt multiplicanda prceter necessitatem." 
t Compare Metaphys. XIII. (M.) 4, p. 1078, b. ed. Berol. ; ibid. 
5, p. 1079, b. 36 ; ibid. I. (A.) 6, p. 987 ; ibid. 9, p. 990, b. ; Ravais- 
son, Metaphysique d'Aristote, III. ii. 2 ; Renouvier, Histoire, II. p. 42. 
To avoid misunderstanding, let me remark that the resemblance 
between Aristotle and the Nominalist lies only in his denying a sep- 
arate existence to universals. " Different philosophers have main- 
tained that Aristotle was a Realist, a Conceptualist, and a Nominal- 
ist, in the strictest sense." — Sir W. Hnmilton. 

X For he speaks of the ideas, now as if they were merely mental 
conceptions, now as independent existences. Stalhaum's Parm. Prol. 
p. 273. And he does not clearly explain ivhere the ideas exist, and 
whether they depend on the Divine Mind, or It upon them. Ibid, 
p. 272. 



I 



LAWS OF THOUGHT. 128 

the other, I can conceive it possible that a sage 
mediation might have reconciled these two great 
epirits ; and Aristotle might have owned that the 
universal notions in his mind might answer to cer- 
tain ideas in the Divine, whilst his illustrious master 
might have confessed that, putting revelation out of 
the question, there is no way to the absolute — to 
knowledge of the idea — except a careful observation 
of and reasoning from the facts we possess, in our own 
mind and in the world around us. Plato indeed was 
an inductive reasoner, not inferior to Bacon him- 
self; though the one confined himself too exclusively 
to the facts of the human mind, and the other to 
those of the external world. The question then 
between Plato and Aristotle, as any one may satisfy 
himself who will refer to the original places in the 
works of the latter, chiefly concerned Method, and 
did not turn so much upon a belief in the existence 
of ideas as upon the right to assume them as the 
ground of teaching. 

It is impossible here to follow out this hint through 
the scholastic controversies, where the nature of uni- 
versal was discussed in connection with religion, as 
it had been in its bearings on science ; but its im- 
portance will be felt in that region also. We must 
distinguish between the opinions, that universals 
cannot possibly exist, and that the attempt to ex- 
plain them as independent natures involves us in 
logical difficulties and contradictions. 

Thus divested of one element of confusion, the 
question -Mdli assume a less repulsive f')rm; but its 
ditiiculties do not disappear, nor is its importance 
lessened. Indeed, at the present day the great divis- 



124 OUTLINE OF THE 

ion between scientific men has assumed this form. 
" We cannot attain truth," say the more bigoted 
followers of Bacon, " except by confining ourselves 
simply to the facts of nature, and their arrangement. 
We must not view them in any theological connec- 
tion ; we must not call in any metaphysical idea to 
assist us in grouping them. We have simply to 
arrange them, using names and language for that 
purpose." Here again the question is regarded as 
pertaining to method ; in other words the existence 
of the Deity, the existence and nature of Ideas, are 
not denied, they are only declined or put aside, 
whilst it is denied strenuously that they can be 
brought in to aid man in the investigation of truth. 
The opinions of such writers as Auguste Comte are 
but the latest exhibition of pure Nominalism, under 
its logical as opposed to its metaphysical form. 
*' We must regard individual things as the only 
realities for us, and language as the means of dis- 
covering and preserving their connection." * 

y^ 

§ 65. Questions about Conceptions. 

When a conception is recalled to the mind, under 
what form does it appear ? Under that of a bare 
word, or of all the marks which we abstracted to 

"*■ Upon the history of Nominalism and Eealism may be consulted 
— Brucker, vols. iii. and vi. ; Tennemann's Manual ; the brilliant Pref- 
ace by Cousin to " Ouvrages inedits d'Abelard," Paris, 1836 ; also 
Cousin, Lefons, 1829, Lef. 9. ; Haure'aii, Philosophie Scolastique, 
1850 ; Hegel, Geschichte, iii. 180. In Degerando, Histoire, i. p. 235, 
there is a good account of the shades of opinion in the two parties. 
Sir W. Hamilton's Reid, p. 405 ; Dugald Stewart, Phil, of Human 
Mind, vol. i. ch. 4, § 2 ; Broivn's Lectures ; Bishop Hampden's Bamp 
ton Lectures, Lecture ii. and Notes. 



1 



LAWS OF THOUGHT. 125 

form it, or of riome single object used as the repre- 
sentative of all the others of the same class? We 
have seen already (§ 25,) that the word, or the array 
of marks, may be employed to recall the conception. 
In any proposition which conveys a definition, we 
have examples of both forms. In such a sentence 
as " honesty is uprightness in all dealings which re- 
spect property," the former of the two conceptions is 
used as a counter (notionis tessera) to represent the 
marks, which the latter explicitly conveys ; in the 
phraseology adopted above, " honesty " is a symboli- 
cal, and " uprightness in dealings which respect 
property " a notative conception. As to the third 
opinion, the understanding, which, for convenience' 
sake, puts symbols for true conceptions, does on the 
same account put examples of a conception instead 
of the conception itself, the singular instead of the 
general. For the notion animal, I think of a par- 
ticular horse or cow ; for honesty, of some honest 
man ; for justice, of some Brutus or Aristides ; for 
city, of London or Paris ; but always with a con- 
scious reservation that there are many points about 
this particular case which are not general, and do 
not belong to the conception. But it will hardly be 
questioned by any, that the understanding can, by a 
somewhat severer self-control, throw aside the par- 
ticular case, and retain only the common marks 
which belong to the whole conception. For we 
must admit the power of abstracting some marks 
from the rest, as the having' life, which is the mark 
of animal, is abstracted from the thousand different 
circumstances of size, shape, colour, food, temper, 
which distinguish animals from each other ; else how 



126 OUTLINE OF THE 

are conceptions formed ? And if we can abstract 
the marks from the accidents, surely we can retain 
them in our grasp when abstracted. 

ii. Are representations of the imagination — ^the 
notion we have of a landscape from some poetical 
description, for example — to be considered as in- 
tuitions or conceptions ? If the description could be 
so complete, and the reader's apprehension so accu- 
rate, that every portion of the landscape were dis- 
tinctly seen, and we could distinguish that scene from 
every other, even from one that resembled it most 
closely, then it would be in accordance with the 
definition we have given (§ 47,) to call it an intui- 
tion. But this, I suppose, is never the case. The 
poet can describe a lake-scene with distinctness 
enough to prevent our having an impression from it 
of any other kind of landscape, as a plain with a 
distant city, or the cliffs of the sea-shore. But still 
the description must be far too obscure to prevent 
our mistakinaj this lake-scene for one closelv resem- 
bling it, or even our recalling some lake we remem- 
ber, to supply the deficiencies of his delineation, 
although we know that we are adopting one scene 
whilst he drew another. He can limit our general 
notion of landscape to some particular species, but 
not to this individual landscape — can reduce our 
" all " to " some," but not to " this." Therefore, such 
an image is a conception, used particularly, i. e. only 
some part of it is called up. It is a representation 
of some landscapes, but not of oTze, to the exciu 
sion of the possibility of confounding it with others 

iii. Can there be abstraction without generaliza- 
tion, as Archbishop Whately maintains ? " Suppose 



LAWS OF THOUGHT. 127 

we are speaking of the King of France," says he; 
" he must actually be either at Paris or elsewhere ; 
sitting, standing, or in some other posture ; and in 
such and such a dress, &c. Yet many of these cir- 
cumstances (which are separable accidents, and con- 
sequently) which are regarded as non-essential to the 
individual.) are quite disregarded by us ; and we 
abstract from them what we consider as essential ; 
thus forming an abstract notion of the Individual. 
Yet there is here no generalization." A great error 
lies hid in this passage — that of not perceiving that 
the power of separating circumstances called essen- 
tial to the individual from those which are not so, 
results from former generalizations. How, do we 
know that "sitting" or "standing" is not essential 
to a king ? How do we know that a crown and a 
robe of state are separable from the King of France ? 
By prior generalization ; by the help of the concep- 
tion we have formed of a king already. If we had 
never known of other kings, or the same king at 
other times, we should have looked on the accidents 
and essentials of the King of France as alike essen- 
tial. We know that "sitting" is not essential, be- 
cause we know that kings sometimes do not sit. 
There is no abstraction without generalization ; and 
in the case before us, we abstract, to refer to a former 
general notion or conception. 

§ 66, Summary. 

The first part of Logic explains that power of the 
mind which groups single objects into classes, so that 
the classes have names and attributes of their own. 



128 OUTLINE OF THE 

Its principles are these : 1. The nature of every 
higher notion is found in the lower ; consequently 
2. The name of the higher may always be applied 
to the lower. Thus man may be called an animal, 
because the marks of life and sensation which dis- 
tinguish animals are found in him. 3. The higher 
notion {genus) includes the lower notion {species) 
with other species, and is therefore of wider exten- 
sion than it. But the species implies more marks — 
has a fuller definition — than the genus ; and is said, 
therefore, to be of deeper intension than it. 4. That 
set of marks which distinguishes any species from 
the other species in the same genus is called its 
Specific Difference. 5. The whole nature of a spe- 
cies is ascertained, and its definition given, when the 
properties of the genus and those which make the 
specific difference are brought together. 6. We as- 
cend from lower conceptions to higher by throwing 
away specific differences, i. e, by abstraction. We 
descend to lower ones by resuming the marks we 
have thrown away, i. e. by determination. 7. In a 
system of subordinate genera each must contain the 
individuals included in the lowest. 8. Coordinate 
species cannot contain the same individuals. 9. The 
conception of an object consists of the aggregate of 
its marks, with the notion of existence superadded. 
10. Singular objects are invariably referred to and 
viewed through general conceptions. 11. A con- 
ception is complete and adequate, when it can be 
resolved at pleasure into its implied marks by defi- 
nition, and into its contained species by division. 
12. Two marks which stand to each other as positive 
and privative, like wise and unwise, are called con- 



LAWS OF THOUGHT. 129 

tradictory, because it would be a contradiction in 
terms to assign them at the same time to the same 
object. Two marks are called contrary, when it is 
known a posteriori by experience, and not a priori 
by the very form of expression, that they cannot be- 
long to the same object, as wise and ivickedy ivarm 
and frozen. 



I 



OUTLINE 



LAWS OF THOL^GHT, 



PART IL 
JUDGMENT. 



Oidifiiav J %p ovre ovrug ovt' EKEtvug Tcpa^iv ovd' anpa^iav d^jAoZ li 
^uv^^evTU, Ttilv uv Tig rdig bvb[taai to. (y^fiara Kspday. — ^Plato. 



JUDGMENT. 



§ 67. Judgment defined. 




VERY act of judgment is an attempt to 
reduce to unity two cognitions. When 
one decides that " Socrates is wise," it 
is that hereafter one may, by combining 
the two notions, think of . " the wise Socrates." 
Again, when one decides that " the world is not 
eternal," it is that hereafter one may refrain from 
combining the two notions as " the eternal world." 

A Judgment then is an expression that two notions 
can or cannot be reconciled — that the marks of the 
one may or may not be henceforward assigned to 
the other.* A proposition is the expression of a 
judgment in words. 

* This definition is rejected by Mr. Mill, Logic,' vol. i. p. 116, seq. 
on the ground that a judgment expresses the agreement of things 
rather than of notions. But the notions are controlled by the things, 
otherwise assent and dissent would be arbitraiy. I am forced to say 
" the day is fine " when the sky is cloudless, because my perceptions 
must correspond with the facts. This correspondence then the 
definition in the text is considered to imply ; and it is retained be- 
cause it is believed to be the only one that includes and describes 
every kind of judgment. But the weight allowed to Mr. Mill's ob- 
jection will depend on the theory of Perception we adopt, and that 



134 OUTLINE OF THE 

Though the truth or falsehood of a judgment, 
and consequently its value, depend upon its cor- 
rectly representing things without us, rather than 
thoughts within us, it is primarily concerned with 
those representations in the mind by means of which 
alone things are brought into the arena of thought, 
whether as single objects or as the ground of abstract 
and general notions. 

Every judgment has three parts : the subject or 
notion about which the judgment is ; the predicate, 
or notion with which the subject is compared ; and 
the copula or nexus, which expresses the mode of 
connection between them. The subject and predi- 
cate are called the terms of the judgment, i. e. the 
extremes or boundaries (termini) which it brings 
together. 

§ 68. Doctrine of Relation in Judgments. 

When we examine such a judgment as " Man is 
a rational animal " (which, trite as it is, will serve 
for our present purpose), we find that the subject 
and predicate are exactly coextensive ; in other 
words, no object comes into the class of rational 
animals which is not also in man, and conversely no 
object comes under man which is not also under 
rational animal. The two conceptions, the one sym- 
bolical the other notative,* are derived from and 
represent the very same class of beings. This equal- 
ity of subject and predicate is an important property 

great metaphysical question we cannot here discuss. See, however, 
Reid, Int. Powers, Essay vi. 3 ; Hamilton's Reid, Appendix C. and 
D.*; Cousin, Histoire de la Phil. Le9on, 24; Edinburgh Reriew, 
vol. lii. Art. " Eeid and Brown." 
*P. 52 



LAWS OF THOUGHT. 135 

of the judgment, for it conveys the power to sub- 
stitute the one conception for the other, at pleasure. 

Other judgments want this property. To say that 
" trees are plants," is to say indeed that no object is 
a tree which is not also a plant ; but then there are 
plants which are not trees ; so that plant and tree 
are not conceptions of equal extent. 

It is true that the copula — the " is " or " are '' 
which couples the conceptions — does not express 
the great difference we have noticed ; being used in 
common language for either relation of the two 
terms. But as the correctness of some trains of 
reasoning depends entirely upon observing the rela- 
tion of coincidence between subject and predicate, 
it is usual to alter the copula in some way, to ex- 
press it, as by saying " is defined to be — is divided 
into — is coextensive with." In the present book, 
instead of the copula " is " or " are," the mathemati- 
cal sign of equality (=) will be employed in affirma- 
tive judgments. in which the predicate is distributed^ 
or taken entire. 

Every affirmative judgment indeed may be re- 
garded as an equation of subject and predicate, as 
every negative is a decision that an equation cannot 
be established. By " All men are mortal " I mean 
that aU men are equal to some mortal creatures ; and 
by " Some plants are poisonous " I mean that a part 
of my conception of plants coincides with a part of 
the conception of poisonous things.* 

* Sir William Hamilton. 



136 OUTLINE OF THE 

§ 69. The Two Predicahle- Classes. 

Logicians have always formed a classification of 
predicates according to the relation in which they 
stand to their respective subjects. We propose to 
give the simplest form to this scheme of Predi- 
cable- Classes, or classes of conceptions which can 
stand as predicates, taking Aristotle's doctrine as the 
basis. 

Every judgment, according to Aristotle, declares 
either a genus, or the property, or the definition, 
or an accident* (-yevog—i6Lov—opog—(jv/ij3e(3T]K6c) of its sub- 
ject. 

The genus is that mark or attribute, which, whilst 
it never fails to accompany the subject, belongs to 
other subjects equally; as in " Envy is a passion." 
The jproperty is that mark or attribute which belongs 
to the subject invariably, and to no other, without 
being the mark that would be used if we had to ex- 
plain the nature of the subject ; as " Man has the 
faculty of speech." Definition is the mark, or aggre- 
gate of marks, that would explain the very nature of 
the subject ; as " A state is a community governed 
by its own laws." Lastly, the accident is an attri- 
bute that happens to attach to the subject, but is 
separable from it ; as " Life is sweet." 

The difference, or that mark or marks by which 
the species is distinguished from the rest of its 

* Top. A. ch. iv. Of the names which A. adopts for the classes, 
yivoi, and perhaps bpog, seems to express rather the extension, the 
others the intension ; but he uses them as having botli powers. The 
common division of Predicable-classes is tliat of Porphyry, intp 
Genus, Difference, Species, Property, and Accident. 



LAWS OF THOUGHT. 137 

genus, does not occupy a distinct position in Aris 
totle's list, but is said to belong naturally to genus 
(uf ovaav ■yevmfiv.'j * The species may be regarded as 
composed, not of the marks of the genus and the 
difference, so well as of those of two concurrent or 
communicant genera ; for the difference is but a 
genus which from its overlapping part of another is 
used as a distinctive mark of that part which it over- 
laps. If (for an easy example) in analyzing our 
notion of "the red-flowering currant" [Ribes san- 
guineum) we regard " currant " as the genus and 
"red-flowering" as the difference, we may also re- 
gard " red-flowering " as a wide geims, wider in fact 
than " currant," and therefore we may say that our 
notion of the plant is formed from the concurrence 
of two genera.f 
V/'' This we suppose to be Aristotle's meaning in con- 
/sidering difference as having the nature of genus. 
But we are now to notice that he examines and ar- 
ranges his four Predicable-classes according to this 
test — Can each of them, without logical fault, change 

* Like the genus, the difference can be predicated of many things 
differing in species. But the genus is predicated hv rcJ ri eari, the 
difference, ev tu tzolov tl. Alex. Aphrod. in Berlin ed. of Arist. ; Top. 
A. ch. IT. 

t Let A be the class of " red-flowering " things, B the class " cur- 
rant;" tl.en X, the part of each which is in the other, will be our 
notion of " red-flowering currant." 




138 OUTLINE OF THE 

places with its subject? In other words, is each of 
them coextensive with its subject or not? The re- 
sults of the test will be apparent from an account of 
each of the classes. 

Definition * is a description which manifests com- 
pletely the nature of the thing defined. Such a de- 
scription would of course enable us to identify the 
subject, and to distinguish it from all other notions. 
And therefore it must be applicable only to the sub- 
ject, otherwise it manifests, not the peculiar nature 
of the thing defined, but its common nature, the 
qualities which it shares with other things. As being 
applicable to the subject and to no other notion, it is 
coextensive with it, and therefore may change places 
with it in the judgment. It is just as true to say 
that " every rational animal is man " as that " every 
man is a rational animal." But if we said that 
" man is a warm-blooded animal," or that " man is a 
civilized animal," neither of them would be a defini- 
tion, nor could the predicate in either become the 
subject, without some limitation. The former is a 
description that applies to more than man, the latter 
to a part only of man ; and of course neither of them 
would enable us to apprehend exactly what man's 
nature was. 

Property! is not easily distinguished from defini- 
tion. Indeed, Aristotle confesses that property (^Idwv'j 
i. e. something peculiar to the subject, and essentially 
its own, is a name which would naturally include 
definition, and would mean some attribute which 
belongs to all the subject and to it only; but he adds 

* Top. A. ch. V. Moi-e fully treated of in Top. Z. passim. 
' Top. A. ch. iv. and v. 



LAWS OF THOUGHT. 1.39 

the special limitation " without declaring the essence 
or nature of the subject." Every quality then which 
belongs to all the subject, and to no other, is a prop- 
erty, provided it be not used in the definition. It 
is coextensive with the subject, and can therefore 
change places with it in the judgment without logi- 
cal fault. Thus, " Man is capable of learning to write 
and speak correctly," might become " Every being 
capable of learning to write and speak correctly is a 
man." 

But this subtle metaphysical distinction between 
the definition and the property is as difficult to main- 
tain as it is unnecessary for the purposes of pure 
logic. How can we rely on being able to separate 
our notion of the nature or essence of a thing from 
the properties which accompany that nature ? Let 
it be the definition of man that he is " a rational 
animal," and the property, that he is " capable of 
speaking correctly ; " and how can we say that the lat- 
ter is not in the essence, yet necessarily follows from 
the essence of man ? It is a part of the essence, for 
" rational " implies it. In like manner, all the prop- 
erties seem to be implicitly contained in every per- 
fect definition. No criterion can be given for dis- 
tinguishing between the essence and the inseparable 
accompaniment of the essence ; and a larger acquaint- 
ance with the nature of things makes it evident that 
what one science regards as a property another 
must consider as essential, and that there is no one 
paramount quality which is absolutely essential 
and can never be degraded to the rank of a prop- 
erty. 

The predisable Genus is a class of which the sub- 



140 OUTLINE OF THE 

jLjct ia a contained part. It declares, though not 
completely, the nature of the subject. A subject 
may be included in many different genera by different 
sets of marks ; a man may be good, brave, rational, 
mortal, fallible, sick, learned, and so on. But some 
of these qualities, as wholly separable from the na- 
ture of man, are to be considered not as genera, but 
as accidents. Genus, as being of the very nature of 
the subject, is inseparable from it. As including the 
subject in common with other species, it is not coex- 
tensive with it. Hence the transposition of the sub- 
ject and predicate in a judgment which predicates 
the genus, cannot take place ; " all roses are plants " 
cannot become " all plants are roses." 

Accident is a quality which belongs indeed to a 
subject, but can be taken away from it without de- 
stroying its nature or essence. We predicate acci- 
dent when we say that " a man is speaking." Acci- 
dent cannot change places with its subject, because 
it does not apply to the whole of that subject and to 
it alone. But a criterion is wanting to distinguish 
between accident and genus or species. It is an ac- 
cident to the people of this country that they were 
born in it ; because we might conceive them to have 
been born elsewhere ; but then it has modified their 
nature or essence, and we understand by Englishman 
not merely one who was born within the four seas, 
but a man of particular feelings, views, and privileges, 
which are parts of his very nature. Here accident 
and genus or property seem to become confused. It 
is an accident too that this nail is rusty and that 
guinea bright, but then it shows that the gold has a 
property — of resisting oxidation — which the iron 



LAWS OF THOUGHT. - 141 

wants, and might serve to place them in two distinct 
species of metals. Aristotle actually speaks of man 
as an accident of the genus animal, although it is 
commonly represented as one of its species;* no 
doubt because we might conceive that species anni- 
hilated without the destruction of the genus. It does 
not appear then that the predicable accident can at 
all times be distinguished from the others, which 
would be a valid objection against retaining the 
doctrine in which it holds a place. 

We propose to abandon, as at least unnecessary 
for logical purposes, the distinction between property 
and definition, genus and accident ; and to form, as 
Aristotle has also done, two classes of predicables ; 
one of predicables taken distributively, and capable 
of becoming subjects in their respective judgments 
without limitation, the other of such as have a differ- 
ent extension. In the former, the predicable has the 
same objects as its subject, but different marks or a 
different way of representing the marks. In the lat- 
ter there is a difference both in the marks and the 
objects. The former may be called Definition, or 
Substitute ; the latter, Attribute.! 

* Cat. vii. 14. In quoting the passage Crackanthorp says : " Om- 
nia inferiora accidentia sunt respectu suorum superiorum." See too 
Cat. vii. 13 ; Pacius, marginal note. 

t Aristotle's arrangement is : — 



Predicables 



Capable of becoming j Definition. 

subjects — convertible. \ Property. 

Incapable of becoming sub- ( Genus, 

jects entire — Inconvertible. I Accident. 



142 OUTLINE OF THE 

§ 70. Definition explained. 
Every predicate which denotes exactly the same 
class of things as the subject, may be called a defini- 
tion. Whether it unfolds the genus and difference, 
or the property, or only substitutes one symbolical 
conception for another, it is useful to mark out for us 
more clearly the limits of the subject defined, and is 
therefore capable of being employed as a definition 
for some thinker or other. Logicians have always 
allowed that in our definitions we are bound to con- 
sider, not merely what is absolutely the explanation' 
of the subject, but what our hearers can adopt as an 
explanation. They would not allow that a defini- 
tion which was conveyed in a metaphor, nor one of 
which the words were strange or obsolete, was prop- 
erly a definition, because it would not be clear* to 
the hearer. They believed that there was an abso- 
ute definition ; but this was to be conveyed with due 
regard to the hearer's needs and attainments. Now 
our reason for enlarging the limits of definition, is 
that any of the predicates we propose to include, 
though not the absolute definition, not the genus and 
difference, may be employed as a definition by some 
particular person, and may to him fulfil the purpose 
of the best logical definition which can be given ; 
and therefore ought, if possible, to be comprehended 
under the same head. Thus, if I wish to define 
" honesty," I may say that it is uprightness in trans- 
actions relating to property, that it is probity, that 
it is the best policy ; and any one of these concep- 

* Aristotle, Top. Z. (vi.) ch. ii. irav yap uaaipeg -b Kara fiETCtpopilt 
Tieyofcsvov nav yap uaade^ to fiij elu&oc. 



LAWS OF THOUGHT. 143 

tions wo aid enable some of my hearers to identify 
honesty, even though that word had not before oc- 
curred in my speech, or been suggested to their 
thoughts. If there were any one paramount con- 
ception, which would be to the minds of all a suffi- 
cient definition of honesty, I should employ that, and 
place it in a class by itself. But this is not the case 
To many a humble thinker, " honesty is the best pol- 
icy," would convey an idea, not adequate indeed, but 
still distinct, when " honesty is uprightness in respect 
to transactions connected with property," would be 
but a string of confused words. Let us then con- 
sider definition as any conception which, from having 
precisely the same sphere as another conception, may 
be used to ascertain its nature and mark out its lim- 
its. And the judgment in which definition is predi- 
cated, we call a substitutive judgment, because it 
furnishes a predicate identical with the subject as to 
sphere or extension, and therefore capable of being 
substituted for it. The subject of a substitutive 
judgment is called also the definitum, or conception 
defined. 



§ 71. Sources of Definition. 

As the subject and predicate of every substitutive 
judgment are coextensive, they may change places 
in the judgment, so that the definitum may become 
in its turn a definition. We may define a concep- 
tion, by exhibiting in our definition its extension, or 
by unfolding its intension, or by the substitution of 
one symbol for another, or one set of marks for an- 
other. It will be found from these principles that 



144 OUTLINE OF THE 

there are six sources from which defiuitions may 
arise, i. From Resolution, when the marks of the 
definitura are made its definition; as in "a pension 
is an allowance for past services." It is not necessary 
that the marks should be completely enumerated — 
that the conception should be strictly adequate — but 
only that the marks should suffice for the identifica- 
tion of the subject, as belonging to it all and to it 
alone ; so that Aristotle's Property would be included 
in it. ii. From Composition, the reverse of the last 
method, in which the definitum, a conception of 
which the component marks are enumerated, stands 
subject to a definition implicitly containing those 
marks ; as, " those who encroach upon the property 
of others are dishonest." iii. From Division, where 
we define the subject by enumerating its dividing 
members ; as, " Britons are those who dwell in Eng- 
land, Scotland, or Wales." All the judgments called 
disjunctives are under this head. iv. From Colliga- 
tion, the exact reverse of the last ; where the dividing 
members of a conception are enumerated in the sub- 
ject, and the divided conception itself added to define 
them ; as, " historical, philosophical, and mathemat- 
ical sciences are the sum (i. e. are all, or equal) of 
human knowledge." This is the form which Induc- 
tive Judgments naturally assume, v. From change 
of Symbol, where both subject and predicate are 
symbolic conceptions, the latter being given as a sub- 
stitute for the former on a principle of expedience 
only; as, " probity is honesty." This is the nominal 
definition of some logic-books. vi. From Casual 
Substitution, where one representation is put for an- 
other on a principle of expedience only, as serving to 



LAWS OF THOUGHT. 



145 



recall the marks, which both possess in common, more 
readily to the hearer's mind ; as, " the science of poli- 
tics is the best road to success in life ; pleasure is the 
opposite of pain." 



Table of Definition. 





By its In- 
tezasion (or ■ 
Marks) 


' being unfolded, 
being reunited, 


= ii. 


Resolution, or 
Definition 
proper. 
Composition. 


t3 

1- 


By its Ex- 


being divided, 


= iii. 


Division. 


tension (or - 








ft 

0) 

o 


Sphere) 


being reunited, 


= iv. 


Colligation. 


a 
o 

< 


By Acci- 
dental Co- - 
incidence 


of a Symbol, 
of Notation, 


= V. 

= vi. 


Nominal Defi- 
nition. 

Accidental Defi- 
nition. 



§ 72. Attribute. 

A predicate, the exact limits of which are not de- 
termined, cannot be used to define and determine a 
subject. It may be called an attribute ; and conveys 
not the whole nature of the subject, but some one 
quality belonging to it. " Metals are heavy," " Some ^ 
snakes are venomous," are judgments in which this 
kind of predicable occurs. 



§ 73. The Common Division of Judgements as to 
Relation. 

The relation in which the subject stands to the 
predicate in a judgment, whether as coincident ojr 
not coincident with it, we call the doctrine of Rela- 

10 



146 OUTLINE OF THE 

Hon; as to which we find that predicates are of two 
kinds substitutes or definitions, and attributes. The 
common account of Relation, which we are bound 
to consider, is somewhat different. 

Judgments are divided, according to it, into three 
classes, the Categorical, the Hypothetical, and the 
Disjunctive Judgment. 

The Categorical Judgment is one in which one 
conception is affirmed to belong or not to belong to 
another ; as, " Men are endowed with conscience," 
" An enslaved people cannot be happy." 

The Hypothetical expresses seemingly a relation 
between two judgments, as cause and effect, as con- 
dition and conditioned ; for example, " If the autumn 
is very dry, the turnip crop is scanty," " K the heart 
is right, so will the actions be." 

The Disjunctive Judgment expresses the relation 
(apparently) of two or more judgments which cannot 
be true together, and one or other of which must be 
true ; as, " Either the Bible is false, or holiness ought 
to be followed ; " or the proverb — "A man is either 
a fool or a physician at forty." 

Categorical Judgments are easily referred to the 
two classes of substitutives and attributives, accord- 
ing as their predicates are or are not equal in exten- 
sion to the subjects. This kind of judgment presents 
little difficulty, after the explanations already given. 

Perhaps our readers may be slow to admit that for 
all logical purposes the hypothetical judgment may 
be treated as a categorical. Yet this is the view to 
which we must adhere, in common with the best 
logicians. In the hypothetical, there are not tw^o 
judgments, but one. In the example, " K the heart 



LAWS OV THOUGHT. 147 

is right, the actions will be so," we neither say that 
any one's heart is right, nor that his actions will be ; 
we do not pass a judgment about either absolutely, 
but we say that if the one is, then the other will be. 
So that what we really decide is that there is a con- 
nection between the two facts ; and the logical copula, 
though not expressed there, has its proper place be- 
tween the two clauses, thus [" the case, fact, or notion 
of the heart's being right] is [a case, fact, or notion 
of the actions being so."] But there are several 
kinds of hypothetical judgments, which have differ- 
ent properties. 

The hypothetical judgment appears, as we have 
said, as two judgments, the former of them, contain- 
ing the condition, being called the antecedent, and 
the latter, containing the effect of the condition, 
being called the consequent. In each of these there 
are two terms, which would give four in all, if one 
of the terms of the antecedent did not sometimes 
reappear in the consequent, when the number of 
distinct terms is of course but three. Now only 
five arrangements of these terms are possible ; in 
four of which there are but three terms, and in the 
fifth, four. 



They are — 



1. If A is B, A is C. 

2. If A is B, B is C. 

3. If A is B, C is A. 

4. If A is B, C is B. 

5. If A is B, C is D. 



148 OUTLINE OF THE 

The following are examples of these formulae : — 

1. If one of the angles of a triangle is a right angle, it must be oppa 

site to the greatest side. 

2. If this be poetry, poetry is worthless. 

3. If animals are creatures with a digestive cavity, polyps are ani- 

mals. 

4. If virtue is voluntary, vice is voluntary. 

6. If the moon exerts her attractive force in the same line as the 
sun, the tides are at the highest. 

The obvious difference between the first four ex- 
amples and the fifth is, that the fifth alone expresses 
two separate facts, brought together as cause and 
effect, whilst in all the rest, from the recun'ence of a 
term in both clauses, it is impossible to separate 
entirely the two things stated. This leads to the ob- 
servation of a real difference in their nature. With- 
out attempting to examine the origin of our idea of 
cause and effect, we may state, as a thing generally 
admitted, that all men are accustomed to regard 
some one fact as the necessary result of another, 
which they have observed invariably to precede or 
accompany it; and that they may learn, however 
different in nature the two facts may appear, to 
identify them so far as invariably to expect the effect 
where they have observed the cause. The vibration 
of a tense wire, and the hearing of a musical note, 
are two distinct facts, yet the one causes the other. 
The drawing of a trigger is a very different fact from 
the sudden death of a healthy man ; yet every one 
knows that under certain circumstances the one will 
infallibly cause the other. The revolution of the 
moon has so little apparent connection with the 
spring and neap tides, that it would be long before 



o^AWS OF THOUGHT. 149 

men observed what is realJy the case, that the posi- 
tion of the moon influences the tide's fluctuations. 
Experience observes that events happen together, or 
in a close succession, and the mind, after adequate 
observations, connects them by its idea of cause. 
Whether this idea be also a part of the experience, 
or one of the primitive constituents of the mind 
itself, even as the eye is a constituent part of the 
body, is a question much debated ; but it need not 
occupy us. We have to remark that two facts, 
which do not resemble one another, between which 
perhaps we once saw no connection, may be insepar- 
ably linked together in our minds, as a cause and an 
effect. And when the connection between them is 
stated, in a hypothetical (that is, a conditional) judg- 
ment, the truth of the statement will entirely depend 
upon the correctness of our observation, since there 
can be nothing in the statement itself to serve as a 
criterion of its truth. In " If A is B, C is D," we 
have no test but the application of our idea of 
cause and effect to the facts for which these letters 
stand. But in " If A is B, A is C," we appeal, not 
to the idea of cause, but to a categorical judgment 
of which we have the materials before us. " If A is 
B, A is C " will be true provided « All B is C " be 
true. " If this is an equilateral triangle, it is also an 
equiangular " must be tried by the rule, " All equi- 
lateral triangles are equiangular." Here is no notion 
of cause ; but a statement of a rule, with the "Bjap- 
position that some one case comes under it. It 
really means, not that one event is caused by an- 
other, but that a conception has certain marks 
which is the function of the categorical judgment. 



150 OUTLINE OF THE 

All judgments apparently hypothetical, but having 
three terms only, may be reduced to categoricals by 
leaving out the terra that is repeated, and using the 
other two for subject and predicate. Thus, " If this 
be poetry, poetry is worthless," becomes, " This 
(poetry) is worthless ; " and " If virtue is voluntary, 
vice is voluntary," means that " Virtue (in so far as 
pertains to the control of the will) is the same as 
vice." But as they have the conditional form, they 
may also be reduced to categoricals in th^ mode 
already described; — "The case of virtue being vol- 
untary is a case of vice being voluntary." The con- 
ditional particle if means, in judgments of this kind, 
" if it should prove that — or, be granted that," since 
the facts exist already, and the supposition refers to 
our knowledge of them. But in the true conditional 
the "if" signifies "if it occurs that," since the fact 
must come about to necessitate the occurrence of 
another fact. 

But whilst conditional judgments differ essentially 
from categoricals, the former affirming the casual 
connection between two distinct facts, and the latter 
declaring that a thing or class of things has some 
property, there is also a sufficient similarity to admit 
of their being identified, for logical purposes. Both 
alike affirm the invariable connection of their two 
terms. By " All the tissues of the body continually 
decay and are reproduced," is meant that wherever 
one "of the tissues of the human body exists, decay 
and reproduction are going on, and cannot be ab- 
sent ; and in like manner, by " If the moon's attrac- 
tion acts against that of the sun, the tides are low," 
is meant that whenever these two heavenly bodies 



LAWS OF THOUGHT. 151 

are found in the supposed position, we find a par- 
ticular state of the tides. In both cases one thinar is 
affirmed to be an accompaniment of another. In 
the categorical, a thing has the mark expressed by 
the predicate ; and in the conditional, a fact has 
another fact for its mark. In the example given of 
the former kind of judgment, we affirm that without 
the notion of decay and reproduction, our notion of 
the tissues of the body would be wrong and incom- 
plete ; in the other example that our notion of that 
position of the heavenly bodies would be incom- 
plete, if we did not take into view its influence on 
the tides. Logic, willing to simplify her formulae, 
and to leave the examination of the idea of cause 
and effect to Metaphysics, reduces the conditional to 
the same rules as the categorical. The formula, 
" The case, fact, or notion of this existing, is, a case, 
fact, or notion of that existing," is sufficient for the 
reduction of any conditional to a categorical. For 
true conditionals, i. e. those where the supposition 
relates to the occurrence of facts, not to our knowl- 
edge of facts, we shall generally say, " The fact of 
his being," &c. ; for the other kinds, " The notion" 
&c. But some variations are admissible. Thus, 
recurring to our examples, we may say, — 

1. The case of one angle of a triangle being a rectangle — is — a case 

of its being opposite to the greatest side. 

2. The admission that this is poetry — would be an admission that 

poetry is worthless. 

3. The statement that animals are creatures with a digestive cavity 

— implies — that polyps are animals. 

4. The notion that virtue is voluntary — impHes — the notion that vice 

is voluntary. 

5. The fact that the moon exerts her attractive force in the same lins 

as the sun — implies — the fact that the tides are at the Irighest. 



152 OUTLINE OF THE 

But let it be noticed that the four first examples 
contain the materials not so much of a judgment, as 
of a perfect argument, of which one of the judg- 
ments is supposed to be true. 

1. Every right angle of a triangle is opposite the greatest side, 
This angle is a right angle ; 

Therefore it is opposite to the greatest side. 

2. This poetry is worthless, 

This poetry is all poetry (i. e. is a fair sample of every kind) ; 
Thei-efore all poetry is worthless. 

3. Animals=creatures with a digestive cavity. 

Polyps have tliis ; 
Therefore they are animals, 

4. Virtue is voluntary. 

Vice (as far as the will goes) is the same as virtue ; 
Therefore vice is voluntary. 

Conditionals may appear either as substitutive or 
attributive judgments. If they set forth some cause 
which not only produces a given eiffect, but is the 
only cause that does so, they belong to the former 
class. " If the moon comes between the sun and the 
earth, the sun will be eclipsed" — is a judgment 
of this kind, for there is no other cause which pro- 
duces that effect ; and therefore we may either say, 
" All cases of the moon's coming between the sun and 
the earth — are — cases of the sun's being eclipsed," or 
the simple converse, " All cases of the sun's being 
eclipsed — are — cases of the moon's coming between 
the sun and the earth." But where the cause stated 
is only one of several which might have produced 
the effect — as in " If it rains, the flower-beds will be 
wet," where the same effect would be produced by 
the falling of dew, or the use of the watering-pot, — 
we cannot employ the simple converse, for the predi- 
'^ate is wider than the subject. We may say, " Al] 



LAWS OF THOUGHT. 153 

cases of its having rained are cases of the flower- 
beds being wet," but obviously not " All cases of the 
flower-beds being wet are cases of its having rained." 
These are attributives. 

Disjunctive judgments may all be referred to the 
head of substitutives ; for the sphere of the predicate 
is just equal to that of the subject, the latter being 
a conception, and the former the same conception 
logically divided (§ 55.). In " Either Shakspeare is 
wrong, or Richard III. was a monster," our meaning 
may be expressed thus — " The possible cases in this 
matter are that Shakspeare is wrong, and that 
Richard III. was a monster ; " which is a substitutive 
judgment. The real premiss in a disjunctive argu- 
ment is not the disjunctive judgment itself, but, as 
will be shown, a certain immediate consequence 
from it. 

§ 74. Doctrine of Quantity, or of the extension of the 
subject in a judgment. 

A judgment is either about the whole of a concep- 
tion, as, " All stars shine," and this we call a uni- 
versal judgment ; or about part of a conception, as, 
" Some lakes have an outlet," and this is a particular 
judgment; or about an intuition, as, " Northumber- 
land House is near Charing Cross," and this is a 
singular judgment. 

For logical purposes we may regard all singulars 
as universals, because they agree in bringing in the 
whole, and not a part, of their subject. So that as 
to Quantity, judgments are either universal or par« 
ticular.* 

* See Wallis's Logic, Thesis i. Further distinctions of judgment! 



154 OUTLINE OF THE 



§ 75. Doctrine of Quality, or the as^reement or dis' 
agreement of subject and predicate. 

Where a judgment expresses that its two terms 
agree, it is called Affirmative ; as, " All planets move 
in an elliptic orbit ; " where it expresses their dis- 
agreement, it is termed negative ; as, " No human 
knowledge is perfect." This part of the judgment 
is its Quality. Although the negative particle is 
not always connected with the copula, but may 
appear in other parts of the sentence, in every real 
negative judgment it belongs only to the copula. 
The two terms are given, and the question always 

as to Quantity have been brought in bv the acuteness of logicians, 
which for philosophical purposes are not very important. The judg- 
ment — "Most men are prejudiced," cannot, it is argued, be consid- 
ered as particular, for it implies not only that some men, but more than 
the half of mankind are prejudiced. These are termed plurative indg 
ments ; and will be mentioned again in examining the syllogism. To 
Professor De Morgan belongs the merit of recalling attention to tliera ; 
and in his elaborate and acute " Formal Logic," p. 325, he inserts Sir 
W. Hamilton's remark upon the use of them, that " aU that is out of 
classification — aU that has no reference to genus and species, is out 
of Logic, indeed out of Philosopher j " that Philosophy seeks to know 
whether all or some or none of a subject comes into a predicate, but 
not whether much or little, for " Philosophy tends always to the \mi- 
versal and necessary," to which this distinction does not seem to 
belong. At the same time the plurative judgment deserves atten- 
tion, as being a possible mode, and as one more proof of the incom- 
pleteness of the doctrine of the syllogism as commonly taught. 

In the same work (p. 142), another class of propositions is men- 
tioned, called the " numerically definite proposition," where the 
number of objects both of the subject and predicate is known and 
specified. The same objection and defence would apply to thera 
as to the plurative judgments ; only that their practical use seems 
even les«, and it is difficult even to invent an example likely t« 
occur 



LAWS OF THOUGHT. 155 

is whether is or is not shall be the connecting link 
between thera. 

But by removing the negative sign from the copula 
and attaching it to the predicate, we may turn the 
judgment into an affirmative of a peculiar kind, 
sometimes called an indefinite,* which is equivalent 
in signification to the negative. Instead of, No 
human knowledge is perfect, we may say with equal 
truth. All human knowledge is wo«-perfect, or im- 
perfect. This license is founded on the law that it 
amounts to the same thing whether we say that our 
subject is shut out from some positive conception or 
included in the cognate privative, for any given sub- 
ject whatever must be found in one of the two. 
(p. 153.) But for logical purposes these indefinite 
judgments may, without inconvenience, be consid- 
ered as aflirmatives. 

To distinguish between negative judgments and 
such as are so only in appearance, we must consider 
whether the sign of negation, not, is meant to affect 
the copula, or whether it really belongs to one of the 
terms. In, " Not to submit would be madness," there 
is no negation, though the sign of it is expressed. 

§ 76. Doctrine of Modalitij. 

The degree of certainty with which a judgment is 
made and maintained, is called its modality; as be- 
ing the mode, or measure, in which we hold it to be 
true. We affirm with very different degrees of as- 
surance, the two judgments, that " An equilateral 
triangle is equiangular," and that " Zeno of Elea 
* By Wolff, Phil. Rat § 209, and Kant, Logik, § 22. 



156 OUTLINE OF THE 

was the inventor of dialectic;" since we can prove 
the former to demonstration, whilst doubts may be 
entertained as to the evidence on which the latter 
rests. Opinions differ as to the place which this 
doctrine ought to hold in Logic. Not without hes- 
itation, it is here excluded from pure, to be discussed 
in applied Logic, on the ground that the modality of 
a judgment is not part of itself, and does not belong 
to the copula, — as seems to be shown by the fact that 
the degree of certainty about the same judgment 
fluctuates in the mind of the same person at differ- 
ent times, and, still more, in different persons, the 
mode of expression remaining unaltered. 

§ 77. Distribution of Terms in Judgments. 

Universal judgments distribute, i. e. introduce the 
whole of, their subject ; particulars do not. In " All 
the fixed stars twinkle " and " No man is wise at all 
times," it is obvious that we are speaking of the 
whole of the fixed stars, and of men, respectively ; 
and therefore each term is distributed. 

Negative judgments distribute the predicate. If 
" No minerals are nutritious for animals " is asserted, 
it means that nothing which is nutritious for animals 
can have the properties of minerals ; and so the term 
" nutritious for animals " is distributed ; and if we 
suppose that only some nutritious things are asserted 
not to agree with minerals, it would follow that some 
other nutritious things might agree with, i. e. might 
be, minerals, so that we might say at the same time 
— " No minerals are nutritious for animals " and 
" Some minerals are nutritious for animals ; " where- 



LAWS OF THOUGHT. 157 

as we know that we meant by the former judgment 
to exclude the possibility of our receiving the latter. 
If the predicate of a negative is not distributed, it 
can have no real negative power ; for if the subject 
is only excluded from one part of the predicate, it 
may be included in some other part. 

Substitutive judgments distribute the predicate. 
Since the predicate in them is used to define the sub-, 
ject, or in other words to mark its exact limits, it 
must itself be definite, and therefore the whole of 
it must be given, otherwise the uncertainty as to 
what part was meant, would make it useless for 
definition. 

~7^We may here remark that an ambiguity attaches 
to some particles which have important duties in 
Logic. The copula is means always exists* but 
when used in a proposition, it expresses an existence 
modified or limited by the predicate ; when employed 
alone, it expresses absolute existence, i. e. that the 
subject is among the class of really existing things. 
Upon this variation a well-known fallacy f was 
founded ; that of arguing that because " Ptolemy is 
dead " (i. e. only exists to us in the way that a dead 
person can, by a remembered or traditionary notion) 
therefore " Ptolemy is " (i. e. has an actual existence 
among other living persons,) which is a very different 
statement. 

Again, the word all in its proper logical sense 
means " each and every ; " but it stands sometimes 
for " all taken together — ^" " All these claims upon 

* See however Waitz, on Organ. 16, a. 12, for the sense of the 
copula in Aristotle, 
t Aristotle, de Soph. Elench. ch. y. iii. Tauchnitz. 



158 OUILINE OF THE 

my time overpower me." Hence may arise in ara« 
biguity ; instead of the all in its logical use, we may 
put every ; but to exercise the same liberty with the 
other sense of it would be absurd. The example 
given could not mean, " Every single claim upon my 
time overpowers me." 

The word some is likewise the cause of confusion, 
in its logical use. In what sense is the " some " of a 
particular proposition to be understood? Does it 
mean, " Some, we know not how many," or, " A cer- 
tain number, which we may have in our thoughts ? " 
Suppose that historical reading leads to the convic- 
tion that " Some democratic governments have ended 
in a tyranny," it may be doubtful whether this result 
includes precisely those democracies which we have 
found in our researches were consummated by des- 
potism, and no others, in which case the conception 
in our minds is definite and precise, though conveyed 
in an indefinite expression, or only expresses that 
this has occasionally happened to democracies, pos- 
sibly to others besides those which we have studied, 
in which case the conception " some democracies " 
would be purely indefinite. The word appears to be 
employed in the two senses of " Some or other," 
and " Some certain," in common language ; and it 
becomes a question in which sense it is to be regarded 
in Logic. 

Now the diflferent steps in attaining knowledge 
are marked by the acquirement of new laws or rules, 
that is to say, of universal judgments, expressing 
that to the whole of a given class of things or 
facts, some mark or property belongs. And where- 
ever a definite number of things is ascertained io 



LAWS OF THOUGHT. 159 

possess a mark, it is the tendency of the mind to set 
them apart from other things that most resemble 
them, by some name which may stand for them both 
in thought and speech, for the sake of making the 
statement universal. If by " Some democracies 
have ended in despotism," we mean simply to assert 
that in three or four countries, with the history of 
which we are familiar, and which we could name, 
this result has occurred, the statement is really uni- 
versal, because our subject is only a species arbi- 
trarily formed of the genus " democracies ; " and we 
ought to say, " The democracies (three or four) whose 
history we have traced." But as our having studied 
them is not of importance enough to found a dis- 
tinction upon, a universal assertion of this kind 
would have no philosophical value ; and by " Some 
democracies end in despotism " we should mean to 
declare that in trying to find the agreement between 
these two terms, we had not succeeded in establish- 
ing the rule, the universal judgment, but that a par- 
tial agreement had appeared, the extent of which, 
though it was discovered from some particular cases, 
was not, so far as we knew, limited to them, but 
remained thoroughly indefinite. Every term then 
which, though indefinitely expressed, refers to a def- 
inite class of things, should be rendered definite. 
Wherever the things denoted by the subject are 
really definite, as having some marks that group 
them in a smaller class by themselves, science re- 
quires that instead of appearing as part of a largei 
class, they should have their own name and posi' 
tion. 



160 



OUTLINE OF THE 



bOMMARY or THE ANALYSIS OF JUDGMENTS. 



s r 



H I 



Quantity 



^ ^ 



.^ •'rt 



Quality ■{ ^ 



Relation -| ^ 






Universal — where the whole subject la 
joined to the predicate, 



or Particular — where part of the subject 
is joined to the predicate, 



Affirmative — where the predicate is de- 
cided to agree with the subject, 



or Negative — where the predicate is de- 
cided not to agree with the subject, 



Attributive — where an indefinite (i. e. un- 
distributed) predicate is assigned to the 
subject, 



or Substitutive — where a definite (i. e. dis- 
tributed) predicate is assigned to the sub- 
ject, wliich may be substituted for it, 
and serve as its definition. 



A-f- 



§ 78. Table of all the Judgments. 

The following table contains examples of the six 
kinds of judgments, with their Quantity, Quality, 
and Relation expressed, and the vowels which mav 
conveniently be used as symbols of them. 



Univ. 


Affirm. 


Attrib 


Univ. 


Neg. 




Part. 


Affirm. 


Attrib, 


Part. 


Neg. 




Univ. 


Affirm. 


Substi. 



LAWS OF THOUGHT. 161 

Sign. Example. Quant. Qcal. Rkl. 

A. All plants grow. 

E. No right action is inexpedient. 

I. Some muscles act without our volition. 

0. Some plants do not grow in the tropics. 

U. Common salt is chloride of sodium. 

Y. Some stars are all the planets. Part. Affirm. Substi. 

An inspection of the table will show that of the 
six judgments there are three of universal and three 
of particular quantity ; that there are four of affirma- 
tive and two of negative quality ; that there are two 
of attributive and two of substitutive relation, whilst 
the two negatives, as denying that either relation 
subsists between the subject and predicate, are un- 
determined as to relation. The vowels in the first 
column are very useful in abbreviating the processes 
of Logic ; for instead of saying that a given judg- 
ment is a universal affirmative judgment, it is suffi- 
cient to say that it is an A, which conveys, to one 
conversant with Logic, the same meaning. The last 
example, of Y, is given in the words best adapted to 
show the distribution of its terms ; but in practice it 
would probably occur as, " Stars include the planets," 
which has precisely the same import. But this form 
of judgment is seldom used,* because, the subject 
being the principal notion in every judgment, it is 
unnatural to put an indefinite (i. e. undistributed) 
conception in the principal place, and a definite (i. e. 
distributed) conception in the place of second impor- 
tance. That notion of which we had the whole be 

The old logicians would have called it, probably, an " inordinata 
propositio," or unnatural proposition — Keckermanni, Log. B. ii. § L 
cap. I., not quite upon the same grounds. Comp. Arist. An. Post, i, 
xxii. 3 ; and Zabarella upon it, p. 909. 
11 



162 OUTLINE OF THE 

fore us, would naturally occur first ; and this, it seems, 
is the psychological principle on which " All planets 
are stars" is a more obvious and natural judgment 
than its converse, " Some stars are all planets." Nor 
is the predicate of Y strictly definitive, since it only 
serves that purpose for a part of the subject. 

§ 79. Table of Judgments according to Sir W. 
Hamilton. 

To the six judgments just given, a very distin- 
guished logician adds two. Extending the doctrine 
of distribution, he says that in negative judgments 
as well as in affirmative, we may speak of — the whole 
of both terms — part of both terms — the whole of the 
subject and part of the predicate — part of the sub- 
ject and the whole of the predicate ; so that there 
are four kinds of affirmatives and four of negatives. 
Putting X and Y to stand for any subject and predi- 
cate, we may exhibit them thus : — 



Sign. 


Affiematives. 


Negatives. 


Sign. 


U. 


All X is all Y. 


No X is Y. 


E 


I. 


Some X is some Y. 


Some X is not some Y. 


6> 


A. 


All X is some Y. 


No X is some Y. 


■n- 


Y. 


Some X is aU Y. 


Some X is no Y. 


0. 



On comparing this table with that given in the 
last section, it will be found that with the exception 
of the two negatives marked ^ and u, each judgment 
here has a counterpart there. Why have we ven- 
tured, in accordance with the practice, it is believed, 
of all logicians, to exclude these two ? 

The answer is, that whilst Sir William Hamilton 



LAWS OF THOUGHT. 163 

gives a table of all conceivable cases c'f negative pred- 
ication, other logicians have only admitted actual 
cases. It is not inconceivable that a man should 
say, " No birds are some, animals," (the jj of the Ta- 
ble,) and yet such a judgment is never actually made, 
because it has the semblance only, and not the power, 
of a denial. True though it is, it does not prevent 
our making another judgment of the affirmative kind, 
from the same terms ; and " All birds are animals " 
is also true. Though such a negative judgment is 
conceivable, it is useless ; and feeling this, men in 
their daily conversation, as well as logicians in their 
treatises, have proscribed it. — But the fruitlessness of 
a negative judgment where both terms are particular 
is even more manifest ; for " Some X is not some 
Y " is true, whatever terms X and Y stand for,* and 
therefore the judgment, as presupposed in every case, 
is not worth the trouble of forming in any particular 
one. Thus if I define the composition of common 
salt by saying " Common salt is chloride of sodium," 
I cannot prevent another saying that " Some common 
salt is not some chloride of sodium," because he may 
mean that the common salt in this salt-cellar is not 
the chloride of sodium in that. A judgment of this 
kind is spurious upon two grounds ; it denies noth- 
ing, because it does not prevent any of the modes of 
affirmation ; it decides nothing, inasmuch as its truth 

* Except of course they represent individuals ; and all that could 
be inferred from such a judgment would be, that its terms were gen- 
eral, not individual — conceptions, not intuitions. Even this, however, 
is provided for, as we know from their being particular, that they 
must be capable of division, and therefore general. " Some Nicias " 
could only be said with propriety if there were several men biarinj 
that name. 



164 OUTLINE OF IHE 

is presupposed with reference to any pair of concep* 
tions whatever. In a list of conceivable modes of 
predication, these two are entitled to a place.* 

* To my objection, that the two weaker negatives have never oc- 
curred in the examination of logical examples, Sir William Hamilton 
replies in the Athenmum (in a letter dated February 25, 1851) as fol- 
lows : " The thorough-going quantification of the predicate (on de- 
mand) in its appliance to negative propositions, is not only allowable, 
is not only systematic, is not only useful, — it is even indispensable. 
For to speak of its very weakest form, that which I call parti-partial 
negation, "-some — is not some;" — this (besides its own uses) is the 
form which we naturally employ in dividing a whole of any kind 
into parts : " Some A is not some A." And is this form — that too in- 
consistently — to be excluded from logic 1 — But again (to prove both 
the obnoxious propositions summarily and at once) — what objection, 
apart trom the arbitrary laws of our present logical system, can be 
taken to the following syllogism ? — 

'All man is some animal, 
Any man is not [no man is) some g^nimal ; 
Therefore some animal is 7iot some animal.' 

Vary this syllogism of the third figure to any other ; it will always 
be legitimate by nature, if illegitimate to unnatural art. Taking it, 
however, as it is : — the negative minor premise, with its particular 
predicate, oflTends logical prejudice. But it is a proposition irrecusa- 
ble ; both as true in itself, and as even practically necessary. Its 
converse, again, is technically allowed ; and no proposition can be 
right of which the converse is wrong. For to say (as has been said 
from Aristotle downwards) that a particular negative proposition is 
inconvertible, — this is merely to confess that the rules of logicians 
are inadequate to the truth of logic and the realities of nature. But 
this inadequacy is reheved by an unexclusive quantification of the 
predicate. A toto-partial negative cannot, therefore, be refused. — 
But if the premises are correct, so likewise must be the conclusion. 
This, however, is the doubly obnoxious form of a parti-partial negar 
live : — 

' Some animal (man) is not some animal (say, brute).' 

" Nothing, it may be observed, is more easy tlian to misapply a 
form ; nothing more easy than to use a weaker, when we are entitled 
to use a stronger proposition. But from the special and factitious 
absurdity thus emerging, to infer the general and natural absurdity 



LAWS OF THOUGHT. 165 



§ 80. Import of Judgments. Extension and 
y^ . Intension. Naming. 

Upon the examination of any judgment which 
appears to express a simple relation between two 
terms, we shall find it really complex, and capable 
of more than one interpretation. " All stones are 
hard," — means in the first place that the mark, hard- 
ness, is found among the marks or attributes of all 
stones ; and in this sense of the judgment, the pred- 
icate may be said to be contained in the subject, 
for a complete notion of stones contains the notion 
of hardness and something more. This is to read 
the judgment as to the intension (or comprehension) 
of its terms (p. 105). Where it is a mere judgment 
of explanation, it will mean, " the marks of the pred- 
icate are among what I know to he among the marks 
of the subject ; " but where it is the expression of a 
new Step in our investigation, of an accession of 
knowledge, it must mean, " the marks of the predicate 
are amon^ lohat I now find to be the marks of the 
subject." 

Both subject and predicate however not only imply 
certain marks, but represent certain sets of objects. 
When we think of " all stones," we bring before us 
not only the set of marks — as hardness, solidity, in- 
organic structure, and certain general forms — by 
which we know a thing to be what we call a stone, 

of the propositional form itself, — this is, certainly, not a logical pro- 
cedure." 

This also occurs, -with a few verbal alterations, in Hamilton's Di» 
rmsions in Philosophy/. Sec. p. 168. 



166 OUTLINE OF THE 

but also the class of things which have the marks, 
the stones themselves. And we might interpret the 
judgment, " All stones are hard," to mean that " The 
class of stones is contained in the class of hard things." 
This brings in only the extension of the two terms ; 
according to which, in the example before us, the 
subject is said to be contained in the predicate. 
Every judgment may be interpreted from either point 
of view ; and a right understanding of this doctrine 
is of great importance. Let it be noticed against a 
mistake which has been reintroduced into logic, that 
all conceptions, being general, represent a class, and 
that to speak of a " general name " which is not the 
name of a class, is a contradiction in terms. But 
this is very diflferent from asserting that a class of 
things corresponding to the conception actually exists 
in the world without us. The conceptions of giant, 
centaur, and siren are all of classes ; but every one 
knows, who realizes them, that the only region in 
which the classes really exist, is that of poetry and 
fiction. The mode of existence of the things which 
a conception denotes is a mark of the conception it- 
self ; and would be expressed in any adequate defi- 
nition of it. It would be insufficient to define " Cen- 
taurs " as a set of monsters, half men and half horses, 
who fought with the Lapithae, so long as we left it 
doubtful whether they actually lived and fought, or 
only were feigned to have done so ; and by some 
phrase, such as " according to Ovid," or " in the 
Mythology," we should probably express that their 
actual existence was not part of our conception of 
them. 

The judgment selected as our example contains 



LAWS OF THOUGHT. 167 

yet a third statement. We observe marks ; by them 
we set apart a class ; and lastly, we give the class a 
name or symbol, to save the trouble of reviewing all 
the marks every time we would recall the conception. 
" All stones are hard," means that the name hard may 
be given to every thing to which we apply the name 
stones. 

All judgments then may be interpreted according 
to their Intension, their Extension, and their appli- 
cation of names or descriptions ; as the following 
examples may help to show. 

A. "All the metals are conductors of electricity " means 

Intension. The attribute of conducting electricity belongs 

to all metals. 
Extension. The metals are in the class of conductors of 

electricity. 
Denomination. The name of conductors of electricity may 

be applied to the metals (among other things).* 
E. " None of the planets move in a circle " means 

Intension. The attribute of moving in a circle does not be- 
long to any planet. 
Extension. None of the planets are in the class (be it real, 

or only conceivable) of things that move in a circle. 
Denomination. The description of things that move in a 

circle cannot be applied to the planets. 
I. " Some metals are highly ductile " means 

Intension. The mark of great ductility is a mark of some 

metals. 
Extension. Some metals are in the class of highly ductile 

things. 
Denomination. The name of highly ductile things may be 

applied to some metals. 
O. " Some lawful actions are not expedient" means 

Litension. The attribute of expediency does not belong to 

some lawful actions. 

* "Among other things." This qualification is required by tbg 
rules of distribution, for metals are only some conductors. 



168 OUTLINE OF THE 

Extension. Some lawful actions do not come into the class 
of expedient things. 

Denomination. The name of expedient cannot be given to 
some lawful ac*;ions. 
U. " Ehetoric is the art of persuasive speaking " means 

Intension. The attributes of the art of persuasive speaking, 
and of Rhetoric, are the same. 

Extension. Rhetoric is coextensive with the art of speaking 
persuasively. 

Denomination. " Tlie art of persuasive speaking " is an ex- 
pression which may be substituted for Rhetoric. 
Y. " The class of animals includes the polyps " means 

Intension. The attributes of all the polyps belong to some 
animals. 

Extension. Tlie class of animals includes the polyps. 

Denoiqination. . The name of polyps belongs to some ani- 
mals. 

§ 81. Explicative and Ampliative Judgments. 

Some judgments* are merely explanatory of their 
subject, having for their predicate a conception which 
it fairly implies, to all who know and can define its 
nature. They are called explicative (or analytic) 
judgments, because they unfold the meaning of the 
subject, without determining any thing new concern- 
ing it. Though they cannot be said to augment our 
knowledge of the subject, the habit of thinking of 
things without realizing all their marks, is so com- 
mon, that judgments in which the marks are predi- 
cated anew are useful to revive our remembrance of 
them ; whilst they are indispensable in explaining to 
others the nature of our subject, of which they may 
not have an adequate notion. If we say that " all 
triangles have three sides," the judgment is explica- 

* Kant, Logik, § 36, and Prolegomena, § 2. Also, for the names 
here adopted, Sir W. Hamilton in Reid's Works. 



LAWS OF THOUGHT. 1 69 

tive ; because " having three sides " is always implied 
in a right notion of a triangle.* 

Judgments of another class attribute to the sub- 
ject something not directly implied in it, and have 
been called ampliative, because they enlarge or in- 
crease our knowledge. They are also called syn- 
thetic, from placing together two notions not hitherto 
associated. For example — " All bodies possess power 
of attraction" is an ampliative judgment; because 
we can think of bodies without thinking of attrac- 
tion as one of their immediate primary attributes. 
But if our knowledge of any object were complete, 
we should conceive it invested with all its attributes, 
and no ampliative judgments would be required. 

We must distinguish between explicative and tau- 
tologous judgments. Whilst the explicative display 
the meaning of the subject, and put the same ma^^er 
in a new form, the tautologous only repeat the sub- 
ject, and give us the same matter in the same form, 
as " Whatever is, is." " A spirit is a spirit." 
Whether in thinking or in teaching, the tautologous 
judgments are useless.f 

Z /v * Such judgments, as declaring the nature or essence of the sub- 
7 ject, have been called " essential propositions." Mill's Logic, b. i. 
ch. Ti. It is, however, a misnomer to call them all " identical prop- 
ositions." " Every man is a living creature " would not be an iden- 
tical proposition unless "living creature" denoted the same as 
"man ; " whereas it is far more extensive. Loche understands by 
idsntical propositions only such as are tautologous — " by identical 
propositions, I mean only such wlierein the same term, importing 
the same idea, is affirmed of itself." (Hum. Under, iv. viii. 3). But 
he condemns the use of vrhat we have called analytic judgments 
likewise (Hum. Under, iv. viii. 4), as adding nothing to real knowl- 
edge ; he would probably admit them as explanatory propositions. 

t Kant, Logik, § 37 ; Locke, Hum. Under, iv. viii. 2. — They may 
accidentally, and by a particular emphasis, become the vehicles of 



170 OUTLINE OF THE LAWS OF THOUGHT. 

emotion or rebuke. The " Sensation is sensation," of Dr. Johnson, 
means, " One cannot help feeling." So too the obvious analytic 
judgments, "A negro has a soul, please your honour," of Sterne's 
Corporal, and " He has no wife," of the agonized ]Macduff, convey a 
pathos from their accidental use, and from the train of judgments 
they suggest, but disdain to express, which their mere logical import 
does not account for. 



OUTLINE 

OF THE 

LAWS OF THOUGHT, 

PAET III. 

SYLLOGISM. EEASONING. 

O fiEV yap (Tu?iXoyi(7/j.bg ek nvuv, egtI te-&evtuv, ugte TJyeiv Ited&I) Ti 
4| avayKTjg tuv k£L{ievuv 6ia ruv KELtdvuiv. — Aristotle. 



SYLLOGISM. EEASONING. 




§ 82. Syllogism. 

HEN the state of our knowledge does 
not warrant us in judging at once 
whether two conceptions agree or diflfer, 
we seek for some other judgment, or 
judgments, that contains the grounds for our coming 
to a decision. This is called reasoning, which may 
be defined "the process of deriving one judgment 
from another." The technical name for that one 
single step of the process, of which the longest chains 
of reasoning are but the repetition, is syllogism, (or 
computation,) a word which has acquired its present 
sense from the resemblance between computation 
proper, i. e. gathering the results of a sura, and that 
gathering of the result of other judgments which we 
call reasoning. A syllogism has been defined " A 
sentence or thought in which, from something laid 
down and admitted, something distinct from what 
we have laid down follows of necessity." * The form 
or essence of a syllogism therefore consists, not in the 

* Aristotle, Pri. An. i. i. I say "a sentence or thought" because 
Myog means both ratio and oratio. The words " laid down and ad- 
mitted " have no exclusive reference to disputation, for we may lay 
down judgments for our own use alone, when there is no disputant in 
the case Trendelenburg and Waitz, on this passage. 



174 OUTLINE OF THE 

truth of the judgments laid down, or of that which 
is arrived at, but in the production of a new and 
distinct judgment, not a mere repetition of the 
antecedents, the truth of which cannot be denied 
without impugning those we have aheady accepted 
for true. 

The new judgment which is to be drawn, and 
which gives occasion for the reasoning process, is 
called, before proof is found, the question or problem, 
and after proof the conclusion. The judgments 
used to establish the conclusion are termed the pre- 
misses ; and the connection between the premisses 
and conclusion, that entitles us to gather the one 
from the other, is the consequence ; as appears 
from the phrases " by consequence," " consequently," 
so often employed in argument. Sometimes the 
conclusion, as following, " by consequence " has 
itself the name of consequence, although consequent 
would be more strictly correct. Latin writers have 
applied the names complexio and connexio to the 
same part of the syllogism. 

§ 83. Immediate and Mediate Inference. 

In some cases we are unable to decide that the 
terms of the question agree with or differ from one 
another, without finding a thkd, called the middhy 
term, with w^hich each of the others may be com- 
pared in turn. This is mediate inference. If one 
suspects that " this liquid is poison," it may be im- 
possible to convert the suspicion into certainty, until 
one has found that " it contains arsenic ;" " contain- 
ing arsenic " will then be the middle term, which will 



LAWS OF THOUGHT. 175 

be compared in a judgment with each of the others 
in turn ; and the whole argument will run, " This 
liquid contains arsenic; and every thing that con- 
tains arsenic is poisonous ; consequently this liquid 
is." We will say nothing at present of the means 
of finding middle terms, although, as in the given 
example, long trains of thought or patient observa- 
tion may be required to secure them. 

But sometimes, instead of a third term, differing 
entirely from the other two, the premiss only need 
contain the two terms of the conclusion, or some 
modification of them. Thus from " All good rulers 
are just" we infer that "No unjust rulers can be 
good," a judgment introducing indeed no new matter., 
i. e. making us acquainted with no new facts ; but 
still distinct from that from which we drew it, as 
representing the matter under a new form. Here, 
for purposes of inference, there are not three different 
terms, because just and unjust, though they stand 
for two separate sets of objects, have a particular 
relation, each implying the existence of the other.* 
Some Logicians refuse the name of inference to this 
and similar processes, on the ground that " there is 
in the conclusion no new truth, nothing but what 
was already asserted in the premisses, and obvious to 
whoever apprehends them." f That the conclusion 
is virtually asserted in the premisses, is true not only 
of these immediate inferences, but of all syllogisms 
whatever; even in the inductive, the mere conse- 
quence — the act of concluding — ^brings in nothing 
which is not known potentially as soon as we havp 
the whole grounds before us. So that the objection 
* See § 59. t M/Z's Logic, b. ii. ch. 1, 2. 



176 OUTLINE OF THE 

proves too much ; as it "would disqualify a set of 
inferences which no one thinks of rejecting. If, 
however, there is absolutely nothing new — if the 
concession of the. premiss is not only a virtual, but 
an actual and express declaration of the conclusion, 
there is no inference, but mere repetition. But who 
can say that "No unjust rulers are good" is a bare 
repetition of " All good rulers are just ? " In the 
one we affirm, in the other deny ; in the one the 
subject of thought is " good rulers," in the other 
" unjust rulers." They are, in these two points at 
least, distinct judgments, and as the passing of the 
one makes it possible, without further observation or 
decision upon facts, to collect the other, there is an 
inference. In many such cases, it is true, the infer- 
ence is so obvious, so certain to occur upon the first 
glance at the premiss, that it seems needless to draw 
it out ; but all the inferences we are about to specify 
are used from time to time, and this entitles them to 
our consideration. 

The same objection would lie against aR attempt* 
to give rules for the immediate inferences, as would 
be brought against a definition of the colour blue, or 
scientific directions for walking ; namely, that the 
things themselves are so simple that we understand 
them perfectly without directions. It is easier to 
discover for ourselves the principle of any case that 
may arise, than to charge the memory with a list 
of all the cases and their laws ; and therefore few 
students will go beyond the simple examination of 
the following sections, which are necessary to thg 
completeness of oar analysis of thinking. 



4 



LAWS OF THOUGHT. 177 

§ 84. Opposition and Inferences depending on it. 

Opposition of judgments is the relation between 
any two which have the same matter, but a different 
form, the same subject and predicate, but a different 
quantity, quality, or relation. Between " No form 
of government is exempt from change," and " Some 
forms of government are exempt from change," 
there is an opposition, called by logicians contradic- 
tory, the rule of which is that one or other of the 
judgments must be true, that no intermediate one is 
possible, and that both cannot be true together. 
Hence it results, that if I lay down that " No A is 
B," I imply the impossibility of laying down " Some 
A is B," or, in technical phraseology, if I posit the 
one I remove the other. And again, the refusal to 
adopt " No A is B," is equivalent to laying down 
that " Some A is B ; " the removal of one implies the 
position of the other. The doctrine of opposition 
has to show what may be inferred as to the truth or 
falsehood of any other kind of judgment, from the 
truth or falsehood of a given one, the subject and 
predicate remaining always the same. Arbitrary 
names, sanctioned by the earliest usage, have been 
given to the relation between each pair of judgments, 
to which some addition has been rendered necessary 
by the new judgments U and Y. But the terms 
chosen are such as convey their own meaning; and 
where it was possible, the well-known names have 
been extended to new relations, instead of introduc- 
ing new ones. 



178 OUTLINE OF THE 



Tjbles of Opposition of Judgments. 

I. 

A . . Contrary . . E . . Contrary . . U 

A ■ ' • ■ ■" 

H % ^ "^rt. "» 

» o°* ••. - ..^ . I 

I . Subcontrary . O . Subcontrary . Y 

n. 

A . Inconsistent . U 



;S ^^ ^ .2 

3 c^ \ p 

M ^ 'p. y 

I . . Subaltern . . Y 

There are five kinds of Opposition ; Contradiclory, 
Contrary, Inconsistent, Subaltern, and Subcontrary. 

Contradictory opposition * is the most perfect, as 
we can infer both from the position of a judgment 
the removal of its contradictory, and from the re- 
moval of the judgment the position of its contra- 
dictory, as has been shown above. ,' It only exists 
between the judgments E and I. Other writers 
describe A and O as contradictories ; but the fact 
is that we cannot tell from the removal of O, 
whether we ought to replace it by A or U. Let 
the O " Some men are not rational animals," be re- 

* Aristotle often called judgments of this kind simply "opposites" 
(avTineiiiEvaL), as if he considered contradictory opposition the oppo 
sition par excellence. Waitz on Org. xi. b. xvi. 



LAWS OF THOUGHT. 179 

moved, i. e. its truth denied, and that removal will 
not establish the A, " All men are (some) rational 
animals." A third judgment is possible, namely, 
that "All men are all rational animals," — the only- 
rational animals there are, and which of these two 
is to apply, cannot be inferred from the O, but must 
be ascertained from the facts of the case. ,/ 

Contrary opposition exists between a^'mative and 
negative judgments which cannot be true together, 
but which may be false together ;(that is, between 
A and E, E and U, E and Y, U and O, and A and 
O. From the position of a judgment we are able to 
infer the removal of its contrary; but the judgment 
may be removed or denied, without the position of 
the contrary. If it is laid down that " All men have 
a right to freedom," it becomes impossible to lay 
down that " No men have a right to freedom ;" but 
of course it does not follow from the refusal to admit 
that " All men have the right," that therefore no men 
have, i 

Inconsistent opposition lies between any two af- 
firmative judgments which cannot be correct together, 
but may be false together jf that is, between A and U, 
U and Y, and A and Y. Here it becomes necessary 
to attain a more precise notion of the difference be- ■ 
tween A and U. Suppose the example of U to be 
" Animals are things endowed with life and sensa- 
tion ; " which means — that " animals " and " things 
endowed with life and sensation " are but two modes 
of representing the same thing, and are therefore in- 
terchangeable. Let the example of A be " All men 
are animals ; " — can we say that this judgment has 
the same properties as the other ? can we put " an« 



18^ OUTLINE OF THE 

imals " wherever " men " should' come into oui 
thoughts? No; "animals" is a very wide class, 
containins: " men " and a vast number of other 
species. We mean by our judgment, not that men 
and animals are just the same things, but that men 
are contained in the wider class aninfals. This re- 
lation might be represented to us by making " men " 
a small circle, within "animals" a large one; whilst 
the relation between subject and predicate in U 
would be best conceived as that of two equal circles 
laid one upon the other. Now every judgment 
which is reaUy A, and not U, i. e. which really has 
an undistributed predicate, means that the predicate 
is wider than, and contains, the subject ; whereas 
every U means as certainly that the predicate is no 
wider than the subject. It is true that we sometimes 
form an A where we might form a U ; as in saying 
that " All men are [some) rational animals," from a 
belief that in a higher state of being, or in another 
planet, there may be rational animals to whom it 
would be improper, from their other characteristics, 
to apply the name of men ; where another, disbeliev- 
ing the existence of any creatures besides men, to 
whom the name could apply, may hold that " All 
men are all rational animals." But this does not 
make the judgment true together. Which is true 
depends upon the facts ; and the reason that two 
persons hold the two judgments together, or one 
person holds them at different times, is that they 
know the facts with different degi-ees of correctness. 
Where the facts judged upon are fairly and fully 
known, an A and a U can never represent them with 
equal correctness, nor can ever be true togethep 
They are inconsistent. I 



LAWS OF THOUGHT. 181 

Subaltern opposition is between any pair of af- 
firmative or negative judgments, when the one has 
fewer terms distributed, that is, taken entire, than 
the other. That in which there is more distribution 
is called the subalternant, and that which has less or 
none, the subalternate ; or they may be termed the 
higher and lower. The inference here is, that when 
the higher is laid down the lower follows ; but 
nothing follows from denying the higher, or laying 
down the lower./ I is the subalternate to A, O to E, , 
I to U, and I to Y ; so that from any A, U or Y, '^^ * , 
follows an I, and from any E, an O. The name of "> 
opposition less properly applies here, as the relation 
of the judgments is really a partial agreement. 

Subcontrary opposition is between particular judg- 
ments, of which one is affirmative and the othei 
negative, viz : I and O, O and Y. The name sub- 
contrary is altogether arbitrary and without mean- 
ing, as the judgments have no real contrariety, but 
rather a presumption of agreement. They are op- 
posed, according to Aristotle, only in the form of 
expression.* If " Some men are wise" be the ivliole 
truth " Some- men are not wise," its subcontrary, 
follows of course ; and it has been ingeniously re- 
marked by Toletus, that in this kind of opposition 
there is not the same subject in the two judgments, 
for we mean in one " Some men," and in the other 
" Some other men." Each pair of judgments may 
be true together ; and I and O cannot be false 
together. The opposition of Y and O, though we 
have not given it a separate name, has these pecu- 

* An. Pri. ii. 15. Ammonius terms them virevavna^, and Boethiui 
tuhcontrarias. 



182 OUTLINE OF THE 

liar properties, that if Y be true, O must be; and 
that they may be false together. To distinguish it, 
we may call it false-contratrj opposition, y 

Two judgments * cannot be called opposites, unless 
the same subject be joined with the same predicate 
at the same time, and under the same circumstances 
in both. " The English are very rich," and " The 
English are not very rich," may be true together, if 
English capitalists are referred to in the former, and 
the public revenue of England in the latter. More- 
over, if the judgment imply an act of comparison 
with some third thing as a standard, the same 
standard must be preserved in its opposite. It is not 
uncommon to hear two such judgments as " This 
house is very large," and " This house is very small," 
pronounced by two people who are comparing it 
with two different standards, the one perhaps with 
his own little cottage, the other with Blenheim or 
Stowe. But these rules resolve themselves into one 
— we must be perfectly sure, by distinctly under- 
standing the subject and predicate, that they are in 
all respects the same in both judgments. 

§ 85. Conversion of Judgments and Inferences 
from it. 

Conversion is the transposition of the subject and 
predicate of a judgment, to form a new one. The 
judgment to be converted is called the convertend, 
and the new one which results from the transposition, 

* Aristotle de Interp. ch. vi. § 5. The Latin logicians say that in 
both judgments we must speak de eodem secundem idem, ad idem, eodem 
mcdo, eodem ier.ipore. 



LAWS OF THOUGHT. 183 

the converse. By conversion, for example, " Some 
salts are fusible," would become " Some fusible sub- 
stances are salts." The converse, as having a differ- 
ent subject of thought (§ 365,) from the convertend, 
is a new judgment, not merely a different statement 
of the convertend ; for it cannot be the same to think 
of " salts," and ascertain what can be attributed to 
them, as it is to think of " fusible substances," and 
ascertain what is to be predicated of them. And as 
the converse depends entirely for its truth upon the 
convertend, we must regard it as an inference from it. 
In right conversion, the quality of the judgment 
is preserved, and each term that was distributed is 
distributed in the converse, but no other. Hence we 
cannot infer from " Some skeptics are vicious " that 
" ^i7 vicious persons ai'e skeptics;" we should dis- 
tribute the term " vicious persons," where the premiss 
exhibited it undistributed. Remembering this rule, 
we may dispense with the common division into 
simple,* and accidental, conversion. The six kinds 

* Simple conversion is where the converse is of the same Quantity 
as the Convertend ; conversion per accidens where the rule of distri- 
bution given above, obliges us to make a particular converse from a 
universal proposition. Aristotle uses the words Kara. au/x!3e(3ijKbc (per 
accidens) to express " with less propriety — improperly," where a thing 
happens to have a name given to it to which it has no natural (Kara 
(pvaiv) title. Boethius applied the same Accidental to an irregular 
conversion, where from our knowledge of the matter we bring out .a 
converse not formally present, as in converting the conclusion of Bra- 
manity in the common books. Thence later writers apply the name 
to what Aristotle has called "particular conversion." Simple Con- 
version is so called properly and naturally, because the proposition 
suffers no other change tlinn a transposition of terras. But Conver- 
sion per accidens is called conversion " less properlj^," because the 
proposition which was universal before is now particular, so that 
there is something more than mere conversion. Berlin Scholia, 175, 
a. 27. ; Waitz on Org. 43, a. 34. ; Sir W. Hamilton, in Mr. Baynes'i 
Analytic, p. 28, note. . 



184 OUTLINE OF THE 

of judgments give the following converses respec- 
tively,— 

A is converted to Y 

E E 

I I 

O V 

V U 

Y A 

Upon the conversion of A it may be remarked, that 
since any judgment and its converse are but two 
fo7"ms of the same matter, i. e. two modes of thinking 
upon the same facts, we ought to be able to recover 
by reconversion the same judgment we at first con- 
verted ; otherwise, if we are obliged to rest con- 
tented with a weaker form, we find that our knowl- 
edge of the facts is less now than when we began to 
convert. By the common rules, A is to be converted 
to I, and that can only be reconverted to L 

The judgment O is usually considered inconverti- 
ble by the ordinary method. But unless we regard 
the essential difference of subject and predicate, it is 
hard to see the reason. Unquestionably in such a 
judgment as " Some substances do not transmit 
light," there, are two terms, the distribution of which 
we know; why then may we not transpose them 
into " No things which transmit light are some sub- 
stances?" Because every judgment should express 
some new truth concerning its subject, which this 
converse appears not to do. The former judgment 
might be the result of experiments, and contains 
substantial information, namely, that there are sub- 
stances not permeable by light. But it is useless to 



LAWS OF THOUGHT. 185 

know that no things which transmit light aie some 
substances, for after all they may be some other sub- 
stances. We ought to treat O then as inconvertible, 
because its conversion seems to be fruitless. 



§ 86. Immediate Inference by Means of Privative 
Conceptions. 

Every conception, we have seen, has a corre- 
sponding conception called a privative. The positive 
conception has marks, but all we know of the priva- 
tive is that those marks are wanting to it. " Un- 
wise," a privative conception, includes whatever 
" wise," the positive, does not. Now it is impossible 
to pass any judgment upon a positive conception, 
without implying others upon the privative ; and 
hence arise many immediate inferences. //• They are 
here submitted in a tabular form,* not of course 
to be committed to memory, but to be carefully ex- 
amined, as a preparation for the practice of supply- 
ing similar ones to any judgments that occur — an 
exercise favourable to acuteness, and readiness in 
interchanging equivalent statements. In th« exam- 
ples, privative words with the prefixed syllable un or 

* Professor De Morgan has furnished the pattern for this Table in 
his "Formal Logic," p. 61 ; the additions here made being such as 
the two additional judgments U and Y made indispensable. No ear- 
lier -writer has taken the troublesto draw out so carefully and clearly 
the various judgments in which privatives may be employed. The 
common books use it in two cases, of which these are examples : 
" All animals feel," then " Nothing which does not feel can be an 
animal ; " " Some judges are not just," then " Some not-just persons 
are judges." Aristotle omits it. Leibnitz (Op. xx. p. 98, Erdmann ed.) 
indicates that there are many forms of privative predication, but doei 
not pursue the subject. 



186 OUTLINE OF THE 

in have been employed, to avoid a multitude of puz- 
zling negative particles. In each group of three 
judgments, the first is the premiss, and the other 
two are inferences from it ; and in the first division 
the premiss of each group contains positive concep« 
tions ; in the second, privative. 

Division I. 

A. All the righteous are happy ; 

Therefore, None of tlie righteous are unhappy ; 
And, All who are unhappy are unrighteous. 

E. iNo human virtues are perfect ; 

Therefore, All human virtues are imperfect; 
And^ All perfect virtues are not human. 

T. Some possible cases are probable ; 

Therefore, Some possible cases are not improballe 
And, Some probable cases are not impossible. 

O. Some possible cases are not probable ; 

Therefore, Some possible cases are improbable ; 
And, Some improbable cases are not impossible. 

TJ. The just are [all] the holy ; 

Therefore, All unholy men are imjust; 
•ind, No just men are unholy. 

Y. Some happy persons are [all] the righteous ; 
Therefore, All who are unhappy are unrighteotis ' 
And No righteous persons are unhappy. 

Divisiox II. 

A. All the insincere are dishonest ; 

Therefore, No insincere man is honest ; 
And, All honest men are sincere. 

E. No unjust act is unpunished ; 

Therefore, AU unjust acts are punished; 
And, AU acts not pimished are just. 



LAWS OF THOUGHT. 187 

I. Some unfair acts are unknown ; 

Therefore, Some unfair acts are not known ; 
And, Some unknown acts are not fair. 

O. Some improbable cases are not impossible ; 
Therefore, Some improbable cases are possible ; 
And, Some possible cases are not probable. 

U. The unlawful is the [only] inexpedient ; 
Therefore, The lawful is the expedient ; 
And, The lawful is not the inexpedient. 

Y. Some unhappy men ai-e all the unrighteous , 
Therefore, No happy men are unrighteous ; 
And, Some unhappy men are not righteous. 

Let it be remarked that the substances we insert 
into these judgments prove that we do not divide 
the whole universe into happy and unhappy, just and 
unjust, &c. but some more limited class of exist- 
ences, such as cases, acts, persons (p. 113). And as 
to the use of such inferences as these, it may be 
noticed that men frequently throw a judgment into 
one of these inferential forms, before they can deter- 
mine upon its reception or rejection. It would be 
natural, upon being assured that " All the righteous 
are happy," to exclaim — " What ? Are all the un- 
happy persons we see then to be thought unright- 
eous ? " Among the above inferences there are no 
mere conversions, so that from any premiss its con- 
verse may be inferred besides. 



§ 87. Immediate Inference by added Determinants. 

Some mark may be added to the subject and 
predicate, which narrows the extent of both, but 
renders them more definite — ^better determined (§ 53), 



188 OUTLINE OF THE 

And from the simple judgment, we may infer that 
which has the additional mark, provided that the dis- 
tribution of terms remain unchanged. Thus, " A 
negro is a fellow-creature; Therefore, a negro in 
suffering is a fellow-creature in suffering." Even 
two judgments* may be amalgamated upon this 
principle ; thus, " Honesty deserves reward, and a 
negro is a fellow-creature ; Therefore, a negro who 
shows honesty is a fellow-creature deserving of 
reward." 



§ 88. Immediate Inference by Complex Conceptions. 

This inference f is parallel to the last ; instead of 
a new conception added as a mark to subject and 
predicate, the subject and predicate are added as 
marks to a new conception. For example, " Oxygen 
is an element, so that the decomposition of oxygen 
would be the decomposition of an element." Here 
again, the terms must be distributed in the con- 
clusion or not, according to their distribution in th(5 
premiss. 

§ 89. Immediate Inferences of Interpretation. 

It has been shown already (§ 78,) that every judg- 
ment may be interpreted in three different ways, ac- 

* See Leibnitz, Op. xix. Theor. 3. Si coincidentibus addantxir 
coincidentia, fiunt coincidentia. Si A=B et L=M erat A + L=B 
+ M. See also Op. xx. 4. 

t See Ze/6««te, Op. xix. Theor. 3. "Si eidem addantur coinci- 
dentia, fiunt coincidentia." Tliis valuable paper -would be much 
clearer, if the g:reat author had distinguished between extension and 
intension. 



LAWS OF THOUGHT. 189 

cording as we regard it from the side of extension, 
or of intension, or of denomination. These are not 
strictly inferences from the judgment, because when- 
ever it is perfectly understood, they are parts of it; 
but relatively to a mind not fully perceiving all that 
the judgment really conveys, they are inferential, and 
we may call them inferences of interpretation. 

Lambert* has given one or two other formulae 
which may come under the same title. " A is B, 
therefore B exists," and " A is B, therefore where A 
is we find B." These may be resolved into one, of 
which an example may show the use. " Howard 
exhibited this high philanthropic spirit, therefore such 
philanthropy really exists," i. e. is not merely imag- 
inary. We make a tacit distinction between our 
notions of real objects and those from imagination or 
from grounds that are palpably false.f Taking our 
notions of Socrates, Heracles, and the Chimasra, we 
see that in the case of Socrates a conviction is im- 
plied that he is a real person, in that of Heracles 
that the representation we have of him is at most 
only partly real, in that of the Chimsera that it is a 
mere invention of the poets. In all our real notions 
we imply the mark of existence, and a neglect of it 
leads invariably to an absurdity. I cannot call it, 
with M. Duval-Jouve,:|: a judgment, because it is 

* Neues Org. i. cli. i. § 259. t See § 375. 

I Logique, § 13. Also Damiron, Logique, p. 12, who regards judg- 
ment as the termination of all the acts of the understanding, whereas 
in the present work it is treated as preparatory to conception, as un- 
dertaken for the sake of more precise and complete notions. But of 
course an "existential judgment" may he formed, as any other ana- 
lytic judgment may, witli any real conception as the subject ; " Man 
exists, the world exists." Compare Raid, Essay vi. oh. i. p. 413, of 
Sir W. Hamilton's Edition. 



190 OUTLINE OF THE 

rather the result of a former judgment; when we 
think of volcanoes, we do not judge that they exist, 
because we have long since done so, and always 
think of them as existent. Farther, every attribute 
of a real object is itself real; and therefore when we 
say that Howard was an exalted philanthropist, we 
of course imply that the existence of exalted philan- 
thropy is established by the fact of Howard's exist- 
ence. But where doubts were entertained that our 
idea of philanthropy had ever been realized, the ex- 
ample before us would have place. 

§ 90. Immediate Inference from a Disjunctive 
Judgment. 

A disjunctive judgment expresses an act of Divis- 
ion, as " The teeth are either incisors, canine, bicuspid, 
or molar teeth." According to the rule of mutual 
exclusion of the dividing members (§ 55) we might 
infer from the judgment just given, that " The molar 
teeth are neither incisors, canine, nor bicuspid." Ac- 
cording to another rule, that the members must com- 
pletely exhaust the divisum, "we infer that the part 
of the divisum not contained in one member, must 
be in some other. " All teeth which are not molar 
are either canine, incisors, or bicuspid teeth." 

FOEMULA I. 

AU A is X Y or Z ; 
Therefore tlie X of A is not tlie Y or Z of A. 

Formula. II. 

AU A is X Y or Z ; 

Therefore the not-X of A is the Y or Z of A. 



LAWS OF THOUGHT. 191 

§ 91. Immediate Inference by the Sum of several 
Predicates. 
After examination of the properties of any subject, 
it is necessary to collect the various predicates which 
have been assigned it, in order to combine them for 
a definition. The definition of copper, for example, 
that it is " a metal — of a red colour — and disagreea- 
ble smell — and taste — all the preparations of which 
are poisonous — which is highly malleable — ductile — 
and tenacious — with a specific gravity of about 8.83," 
is the result of as many different prior judgments 
as there are properties assigned. From a sufiicient 
number of judgments in A, having the same subject. 
a judgment in U may be inferred, whose predicate is 
the sum of all the other predicates. } 

§ 92. Concluding Remark. 

Whilst it is at once admitted that these immediate 
inferences — syllogisms of the understanding as they 
are called by Kant, to distinguish them from the 
mediate syllogism of reason — are obvious enough 
when they appear singly, the great number and 
variety of them may be thought a sufiicient reason 
for examining them. Could any person not accus- 
tomed to exercises of this kind, draw out fully all his 
own meaning, when he utters the simplest proposi- 
tion ? The judgment " All men are mortal," (a plain- 
er cannot be found,) tells us — that man is one species 
in the class of mortal beings — that the mark of mor- 
tality should always accompany our notion of man — 
that the word mortal is a name which may rightly be 



192 OUTLINE OF THE 

given to man — that, if all are mortal, any one mar. 
is — that any statement which affirms that no men 
are mortal must be quite false — that even the state- 
ment that some men are not mortal is equally false — 
that since man is contained in the class of mortal 
things, which is a wider class, it would be wrong to 
say all mortal things are men — that, however, the 
assertion " Some mortals are men " would be true 
enough — even " Some mortals are all men " — that 
no men can be immortal — that any immortal beings 
must be other than men — that mortality really exists, 
being found in man, whom we know to exist — that 
a man with immortal hopes is a mortal with immor- 
tal hopes — ^that (since heaven is immortality) a man 
expecting heaven is a mortal looking for immortality 
— that he who honours a man, honours a mortal. 
Thus from this simple judgment fourteen judgments 
have unfolded themselves, or, as some would say, the 
judgment has been put in fifteen different ways, in 
the last three of which only is any new matter intro- 
duced. And yet any man of common sense would 
say that his proposition really implied them. 



§ 93. General Canon of Mediate Inference. 

The law upon which all mediate inference depends 
may be thus expressed. The agreement or disagree- 
ment of one conception with another, is ascertained by 
a third conception, inasmuch as this, ivholly or by the 
same part, agrees with both, or ivith only one of the 
conceptions to be compared. The mediate syllogism, 
or (as it is usually called) the syllogism, is a com- 
parison of any two notions with a third in order to 



LAWS OF THOUGHT. 193 

ascertain whether they agree or not. Suppose the 
question is whether this disease is mortal ; in order to 
ascertain the agreement of the two notions, so that 
we may say " This disease is mortal," we find a third 
notion, that it is a consumption, which we know to 
be mortal, and then the whole syllogism will be 

All consumptions are mortal, 
This disease is a consumption ; 
Therefore it is mortal. 

All the properties of a syllogism depend upon the 
Canon just laid down ; as will be seen when they are 
enumerated. 

1. A syllogism will contain iJiree notions and no 
more, namely, the two whose agreement or disagree- 
ment we strive to ascertain, and the third which we 
employ as a means of doing so. They are called 
terms ; and the third notion, interposed between the 
others in order to compare them, is the middle term, 
whilst the other two may be called, from their place 
in the concluding judgment of the syllogism, the suh- 
iect and predicate. 

Formerly, the subject of the conclusion was called 
the minor term, and the predicate the major, because 
in one form of inference, supposed to be the most 
perfect, the major was by its position most extensive, 
and the minor least ; thus, in the syllogism " All men 
are mortal, Socrates is a man, therefore Socrates is 
mortal " — mortal, the major term, is more extensive 
than Socrates, the minor ; for, in mortal, we include 
Socrates and all other men. But in negative infer- 
ence it is impossible to ascertain the comparative 
extent of the terms. If the conclusion were " No 

13 



194 OUTLINE OF THE 

beasts of prey are ruminant," it would be impossible 
to ascertain which term were the more extensive, — 
whether "beasts of prey" applied to more objects 
than ruminant — inasmuch as the judgment itself 
declares that they have nothing to do with one an- 
other, and one cannot therefore be applied to meas- 
ure the other. The so-called major term might hap- 
pen to be a good deal less than the minor. When 
the concluding judgment is particular, the same ab- 
surdity attaches to the names. In " Some brave men 
are prudent" it is impossible to say whether "brave 
men " or " prudent men " is the more extensive term. 
The names of major and minor then are only descrip- 
tive, when applied to some particular forms of syllo- 
gism. But they are so interwoven with logical 
phraseology, that it will be better occasionally to 
annex them in a parenthesis to the less objectionable 
ones. 

2. A syllogism must contain three judgments and no 
more. Since it contains three terms, each of which 
is to be compared, once only, with every other, there 
would be three acts of comparison, each expressed 
by a judgment. Three terms cannot be joined in 
more than three pairs without repetition. 

The two judgments in which the middle term oc- 
curs, are called the premisses, -and the remaining one 
the conclusion. That premiss in which the predicate 
(major term) is compared with the middle, was for- 
merly called the Major premiss, and the other, in 
which the subject (minor term) occurs, was the Minor 
premiss. The former was also sometimes called the 
Proposition, and the latter the Assumption, and 
sometimes the Subsumption. But all these name? 



LAWS OF THOUGHT. 195 

are inconsistent with the wider view of inference now 
taken ; and it will be sufficient to call the premisses 
first and second^ the first being always that in which 
the predicate of the concluhion occurs, whether it 
stands first in order or not. 
/)> 3. One premiss at least must be affirmative. The 
Canon provides that one term at least must agree 
with the middle, that is, must be united with it in an 
affirmative judgment ; and without this there can be 
no inference about the two terms which are to be com- 
pared. With the premisses " No rash man can be 
a good general, and Xenophon was not a rash man," 
we could neither have the conclusion that Xenophon 
was a good general, nor that he was not. The prem- 
isses afford no data for discovering in what sort of 
judgment the terms Xenophon and good general may 
come together. 

4. The worst relation of the tivo terms with a thirds 
that may he established in the prenlisses, shall be ex- 
pressed in the conclusion. Now the best and most 
intimate relation of two terms is that of absolute 
identity of matter, as in " An animal is a being with 
life and sensation ; " the next exists where the whole 
of one term coincides with part only of the other, as 
in " All organized structures decay ; " the lowest re- 
lation, where part of one term coincides with part of 
another, as in " Some flowers are blue." If the two 
premisses express two different relations, the conclu- 
sion must follow the inferior. Thus, "All triangles 
— figures with three sides, A B C is a (some) trian- 
gle, Therefore A B C is a (some) figure with three 
sides ; " where the chief predicate though distributed 
in the premiss is not in the conclusion. The worst 



196 OUTLINE OF THE 

positive relation then which the premisses contain, is 
all that can be inferred in the conclusion. 
V 5. On a similar principle, if one of the premisses be 
negative^ the conclusion must also be negative. The 
Canon only supposes two conditions, under one of 
which an inference must be made ; that of agree- 
ment of two terras with a third, expressed by affirma- 
tive premisses, and consequent agreement of the two 
terms, expressed by an affirmative conclusion ; and 
that of agreement of one term and disagreement of 
another, with the thu'd term, expressed in an affirma- 
tive and a negative premiss, and consequent disa« 
gi-eement of the two terms, expressed in a negative 
conclusion. The latter condition obtains wherever 
there is a negative premiss, and therefore the conclu- 
sion will also be negative. 

6. The comparison of each of the two terms must 
be either ivith the lahole, or with the same part, of 
the third term. And to secure this (i) either the 
middle term must be distributed in one premiss at 
least, or (ii) the two terms must be compared with 
the same specified part of the middle, or (iii) in the 
two premisses taken together the middle must be dis- 
tributed and something more, though not distributed 
in either singly. 

The wise are good, 

Some ignorant people are good ; 

Therefore, Some ignorant people are vrise. 

This is only a syllogism in appearance, for the two 
terms have only been compared with part of the 
third term good ; if the wise are some good people, 
and some of the ignorant are some other good people, 
we have compared with two different parts of a 



LAWS OF THOUGHT. 197 

term, which is the same as using two different terms 
— a condition not contemplated by the Canon, and 
one under which there can be no inference whatever. 
But in the next example (i) the two terms meet upon 
common ground in the third term, because the whole 
of it is once introduced. 

All the mineral acids are poison, 
Spirit of salt is a mineral acid ; 
Therefore it is a poison. 

Here, to whatever portion of the class of " mineral 
acids " we refer " spirit of salt," it must be a poison, 
because the whole class of mineral acids was brought 
in as poisonous, so the inference is good. If the first 
premiss were " half the mineral acids are poisons " 
there would be no inference, because the " spirit of 
salt" might be in the other half. There would be 
a comparison with two different parts only of a third 
term. 

The next example (ii) secures a comparison with 
the same part of a third term, not indeed by bringing 
in every part of it, but by specifying which part is 
intended in both premisses alike. 

Certain sciences are classificatory, 

These sciences=Mineralogy, Botany, and Zoology; 

Therefore Mineralogy, Botany, and Zoology are classificatory. 

The same part of the term sciences being used, 
the other two terras must agree. But it is more 
correct to regard " certain sciences " as the whole of 
a smaller term (§ 74), than as the part of a larger, 
sciences in general. The word " certain," marks it 
off so definitely that we may consider it a distinct 
conception. 



198 OUTLINE OF THE 

In the next example (iii), that unusual mode of 

distribution is seen, which is gathered from the two 

premisses combined, although neither contains it 

separately. 

Three-fourths of the army were Prussians, 
Three-fourths of the army were slaughtered ; 
Therefore some who were slaughtered were Prussians. 

For, even supposing that the whole of that fourth 
that were not Prussians, but (say) Austrians, were 
slaughtered, there still remain two-fourths, mentioned 
in the second premiss as slaughtered, who must have 
been Prussians. And this kind of inference may be 
drawn wherever the mode of expression satisfies us 
that something more than all the middle term has 
been mentioned in the premisses ; the extent of the 
agreement between the terms of the conclusion being 
exactly measured by the excess, over and above the 
whole of the middle term. Thus, " three-fourths of 
the army," taken twice, make six-fourths, so that the 
terms of the conclusion agree to the extent of two- 
fourths at least of the middle term. Let these three 
lines represent the terms. 

Prussians [ 

Army 1 | I I I 

Men slaughtered I 



It appears that the middle line, for two-fourths of 
its length, runs parallel with both the others, and for 
that distance, therefore, they run along with each 
other. 

7. Neither term of the conclusion must he distributed^ 
unless it has been so in its premiss. For, the result of 
the comparison as stated in the conclusion must not 
be greater than the comparison itself as made in the 



LAWS OF THOUGHT. 199 

premisses ; if therefore all of a term appears in the 
conclusion as agreeing with another, a comparison 
of all of it with the middle must have been made in 
the premisses. 

Such an inference as , , 

Pittacus is good, ' " '■ '' :Avf^-6-^«^ 

Pittacus is wise, 

Therefore all wise men are good, 

is faulty, because the premisses do not contain " all 
wise men." 

These seven general rules of syllogism are not new 
principles, to be studied as the complement of the 
Canon. They are directly evolved from it, and are 
only so many cautions to employ it properly. The 
K-ule of Syllogism is one and one only, but its con- 
sequences are various, and they are developed in the 
general rules.* 



^ 



§ 94. Order of the Premisses and Conclusion. 

Although an invariable order for the two premisses 
and conclusion, namely, that the premiss containing 
the predicate of the conclusion is first, and the con- 
clusion last, is accepted by logicians, it must be 
regarded as quite arbitrary. The position of the 
conclusion may lead to the false notion that it 
never occurs to us till after the full statement of 
the premisses ; whereas, in the shape of the problem 

■* They may be remembered by the following hexameters : — 

Distribuas medium, nee quartus terminus adsit, 
TJtraque nee prscmissa negans [nee particularis] 
Sectetur partem conclusio deteriorem, 
Et non distribuat, nisi cum prsemissa, negot^a. 



200 OUTLINE OF THE 

or question it generally precedes them, and is the 
cause of their being drawn up. The premisses 
themselves would assume a different order accord- 
ing to the occasion. It is as natural to begin with 
the fact and go on to the law, as it is to lay down 
the law and then mention the fact. " I have an offer 
of a commission ; now to bear a commission and 
serve in war is (or is not) against the divine law ; 
therefore I am offered what it would (or would not) 
be against the divine law to accept." This is an 
order of reasoning employed every day, although 
it is the reverse of the technical ; and we cannot 
call it forced or unnatural. The two kinds of sorites, 
to be described below, are founded upon two differ- 
ent orders of the premisses ; the one going from the 
narrowest and most intensive statement up to the 
widest, and the other from the w^idest and most ex- 
tensive to the narrowest. The technical order can- 
not even plead the sanction of invariable practice.* 

* " In confirmation of the doctrine that tlie common order of the 
premisses should be reversed, may be added, what not one of its 
modern advocates seems to be aware of, that this, instead of being 
a novel paradox, is an old, and imtil a comparatively recent period, 
an all but universal practice. It is not even opposed by Aristotle. 
For to say nothing of certain special recognitions by him of the 
legitimacy of this order, his usual mode of stating the syllogism in 
an abstract or scientific form, affords no countenance to the prior 
position, in vulgar language of what logicians caR the major propo- 
sition. Aristotle is therefore to be placed apart. But in regard to 
the other ancieat logicians, who cast their syllogisms in ordinary 
language, I am able to state as follows ; and this in direct contra- 
diction not only of the implicit assumptions of our later logicians, 
but of the explicit assertions of some of the most learned scholars of 
modern times ; that the Greeks (Pagan and Christian, Peripatetic, 
Academic, Stoic, Epicurean, and Skeptic), down to the taking of 
Constantinople, with very few exceptions, placed first in syllogistic 
order what is called the minor proposition The same was done by 



LAWS OF THOUGHT. 201 

Neither the school of logicians who defend it, noi 
those who assail it, take a comprehensive view of 
the nature of inference. Both orders are right, 
because both are required at different times. The 
one is analytic, the other synthetic ; the one most 
suitable to inquiry, and the other to teaching. 

^ 95. The Three Figures. 

Every syllogism is said to be in one of three 
figures, according to the position of the middle term 
in the premisses. This may be the subject of the 
first premiss (major) and the predicate of the second 
(minor), in which case we say that the syllogism is 
of the First Figure : or it may be the predicate of 
both, which constitutes a syllogism of the Second 
Figure : or the subject of both, which gives the Third 
Figure. Thus, 



I. 


II. 


III. 


M P 


P M 


M P 


S M 


S M 


M S 


S P 


.-. S P 


.-. S P 



It has been usual to call the first figure the most 
perfect, because it exemplifies most directly a certain 
law of syllogism called the dictum de omni et nullo. 
The law is to this effect * — " Whatever is affirmed 

the Arabian and Hebrew logicians." [I may add the Hindu Gotama 
to these anthorities.j "As to tlie Latins they, previous to the sixtli 
century, were in unison with the Greeks. To the authority and 
example of Boethius I ascribe the change in logical practice. He 
was followed by the Schoolmen, and from them the custom has 
descended to us." — Sir William Hnmilton. 

* Aristotle, Cat. ch. 5. Kant puts it Nota notce est nota rei ipsius, 
viewing the intention of the judgments. Leibnitz, Contentum contenti 



202 OUTLINE OF THE 

or denied of a class, may be affirmed or denied of 
any part of that class;" so that if one affirms of 
plants that they require light, one may affirm it also 
of sunflowers, as a part of the class of plants. This 
would requii-e three judgments, one to state what we 
meant to affirm of the class — " All plants need light;" 
— a second to mention something as part of the class, 
" Sunflowers are plants ; " and a third to affirm the 
same of the part as had been affirmed in the outset 
of the whole ; " Sunflowers require light." These 
three judgments, it will be found, have their terras 
arranged according to the first figure. And on the 
assumption that the dictum de omni et nullo was the 
paramount law for all perfect inference, and therefore 
the first figure was alone perfect,* rules have always 
been given for reducing, as it is termed, every syllo- 
gism in the less perfect figures to the first. This can 
readily be done by changing the order of the terms 
by conversion (§ 83), or, in the few cases in which 
conversion will not apply, by substituting a priva- 
tive for a positive judgment (§ 84), and then convert- 
ing. But the question was raised — is the dictum the 
sole law of perfect inference ? Is it not simply an 
account of the process of the first figure, and might 
not each of the other figures have its dictum too ? 

est contentum continentis, viewing (I think) their extension. Leib, 
seems to employ includere for the Aristotelian v-upxeiv, the word 
that refers to the intension of terms ; but he does not sufficiently 
distinguish between the two. 

* Aristotle, Pri. An. i. ch. 5 and 6. Kant, in a little Tract, g^es 
over the same ground, contending that all the figures but the first, 
require the converse of one or other of the judgments to be inserted, 
to make them pure and natural acts of reasoning. My reason for 
dissenting will be given in the text. 



LAWS OF THOUGHT. 203 

The discovery of new dicta* put the piocess of re- 
duction in a new light. Each of the figures was 
found to have its own functions, and an attempt to 
bring the two last to the first figure, only spoilt them 
as examples of their own rules. S,eduction was 
therefore unnecessary. 

We must not suppose that the division of syllo- 
gisms according to the figures, is a mere useless 
subtlety, the result of an arbitrary attempt on the 
part of logicians to display the middle term in every 
possible position. For, first, the premisses we choose 

* These are not introduced into the text, because they belong to a 
system of Logic in which no affirmative judgment was held to dis- 
tribute its predicate, and in which, to comply with the general rules 
of syllogism, the second figure must always have a negative conclu- 
sion, and the third a particular. With our present enlarged list of 
judgments, they would have a very partial application. However, 
to illustrate the older treatises they are here given. In the 1st Fig. 
the dictum given above. The Fig. is useful in arguing from a gen- 
eral to a specific statement. For tlie 2d Fig. the dictum de diverso — 
"if one term is contained in, and another excluded from, a third 
term, they are mutually excluded." Useful for showing the differ- 
ences of things, and preventing confusion of distinct conceptions. 
For the 3d Fig. the dictum de exemplo — " Two terms which contain a 
common part, partly agree, or if one contains a part Avhich the other 
does not, they partly differ." Useful for bringing in examples, and 
for proving an exception to some universal statement. Thus, if it 
were stated that all intellectual culture improved the heart and con- 
duct, it would be natural to say, in this Figure, '' Mr. So and So does 
not act as he ought, yet Mr, So and So is a person of cultivated 
mind, therefore one person at least of cultivated mind does not act 
as he ought." See Keckermann, Logic iii. ch. 7, 8, and 9. Also 
Lambert, N. Org. i. iv. §, 229. But Mr. Mill is in an error, shared by 
Buh^e (Geschichte, vi. 543,) and Troxler (Logik, ii. p. 62,) in thinking 
that Lambert invented these dicta. More than a century earUer, 
Kechermann saw that each Figure had its own law and its peculiar 
use, and stated them as accurately, if less concisely, than Lambert. 
Kechermann however ignored the 4th Figure, and Lambert's explana- 
tion of that may be new. 



204 OUTLINE OF THE 

to establish some conclusion by, may be judgments 
to which we are so accustomed, that it would be un- 
natural to take their converse instead, which might 
be requisite to bring them into the first Figure. It 
makes some difference whether " Kings can do no 
wrong" is to be the judgment, or the much more 
awkward form " Some persons who can do no wrong 
are kings." But, next, it did not escape Aristotle 
that the more extensive of two terms ought to be the 
predicate, that the genus should be predicated of the 
species. This is the natural, though not invariable, 
order ; and it is worthy of remark that in negative 
judgments, where from the negation the two terms 
cannot be set together to determine their respective 
extension, if, apart from the judgment, we know that 
the one is a small and the other a large class, the one 
a clearly determined and the other a vague notion, 
we naturally take the small and clearly determined 
conception for our subject. Thus it is more natural 
to say that " The Apostles are not deceivers," than 
that " No deceivers are Apostles." So that, if our 
minds are not influenced by some previous thought 
to give greater prominence to the wider notion, and 
so make it the subject, reversing the primary order, 
the figure of the syllogism will be determined by the 
extension of the middle term. If this term is ob- 
viously wider than the other two, the second will be 
the natural figure, because there it will be predicated 
of both. If, again, it is obviously narrower than 
both, the thnd, in which it can stand twice as sub- 
ject, will be the natural figure. Thus, when it was 
desirable to show by an example that zeal and activ* 
ity did not always proceed from selfish motives, the 



LAWS OF THOUGHT. 205 

natural course would be some such syllogism as the 
following. 

The Apostles sought no earthly reward, 
The Apostles were zealous in their work ; 
. • . Some zealous persons seek not earthly reward. 

Admitting that where the extension of the concep- 
tions is not very different, either of them would stand 
subject as well as the other, we contend that since, 
in some cases, natural reason prescribes the thiid fig- 
ure or the second, and rejects the first, the doctrine 
of the distinction of three figures is not a mere arbi- 
trary invention, but a true account of what takes 
place in the mind. 

§ 98. Special Canons of the Figures. 

Although the Canon of Syllogism applies suffi- 
ciently to all the figures, it is possible to modify it so 
as to comprehend the order of the terms in each 
figure. 

Canon of the First Figure. 

The agreement or disagreement of a subject and 
predicate, is ascertained by a third conception, predi- 
cate to the former and subject to the latter ; inasmuch 
as this wholly or by the same part agrees with both, 
or with one only, of the conceptions to be compared. 

Canon of the Second Figure. 
The agreement of tv/o concepti'^ns is ascertained 



206 OUTLINE OF THE 

by a third conception, which stands as predicate to 
both ; inasmuch as this wholly, or by the same part, 
agrees with both, or with one only, of the concep- 
tions to be compared. 

Canon of the Third Figure. 

'The agreement of two conceptions is ascertained 
by a third conception, which stands as subject to 
both ; inasmuch as this wholly, or by the same part, 
agrees with both, or with one only, of the concep- 
tions to be compared. 

§ 97. The Fourth Figure. 

Besides the three that have been given already, 
only one other combination of the terms of a syllo- 
gism is possible, namely, where the middle is predi- 
cate of the first (major) and subject of the second 
(minor) premiss. The introduction of this combi- 
nation as a fourth figure, is attributed to Galen on 
the authority of Averroes.* It would fall into this 
form — 

P M 

M S 
.-. S P 

* The words of Averroes are Et ex hoc planum, quodjigiira quarta, de 
qua rr,eminet Galenus, non est syllogismus super quern cadet iiaturaJiter cogi- 
tatic. (In iPrich. viii. vol. i. p. 63.) I liave inspected the Dialectic 
of Galen, published for the first time at Paris in 1844, by Minoides 
]\Iynas, a Greek, from a MS. of tlie eleventh century found in the 
East; and am of opinion — that Galen did not adopt the fonrf/i figure, 
and that an occasional transposition of the premisses in the 1st figure 
may have led to the erroneous belief that he did. That his moiern 
editor confounds tlie 1st and 4th figures is beyond dispute. 



LAWS OF THOUGHT. 207 

Many logicians have condemned the use of this 
figure. It is described as a mere perversion of the 
first, in which the proper conclusion does not appear, 
but the converse of it, gained by immediate inference 
(§ 83). The meaning of this will appear from an 
example (taken from Abp. Whateiy's Logic). 

What is expedient is conformable to nature, 

What is conformable to nature is not hurtful to society, 

What is hurtful to society is not expedient. 

Here it is contended that the mind naturally expects 
the converse of the conclusion, — What is expedient 
is not hurtful to society, — which would bring it at 
once to a syllogism in the first figure, and that we 
tacitly draw the proper conclusion before passing on 
to the unnatural one. But whilst it is plain that such 
a conclusion from such premisses disappoints the ex- 
pectation, we are unwilling to admit that there is 
any interpolation of a judgment, without some good 
reason, especially as Kant supposed the same sort of 
process to have place in the second and third figures 
also, where it is certainly not required. The reason 
now to be given for dismissing the fourth figure as 
really an indirect way of stating the first, has not, it 
is believed, been pointed out before. The subject 
and predicate, we remarked, are different in order of 
thought, the subject being thought of for itself, and 
the predicate for the subject. Now in the first figure, 
the subject of the conclusion was a subject in the 
premisses, and the predicate was a predicate, so that 
the order of thought is strictly preserved. So to 
speak, we do not depose a subject, and set up a predi- 
cate in its place. No primary thought becomes sec 
ondary, nor any secondary primary. 



208 OUTLINE OF THE 

All M is P 

AU S is M 
.-. All SisP 

The conclusion no way disturbs the ord,er of terms 
established in the premisses. But in the second fig- 
ure, the order is somewhat disturbed ; the subject of 
the conclusion was indeed a subject in the premisses, 
but the predicate was not a predicate. 

No P is M 
All S is M 
.-.No SisP 

This makes the figure one degree less natural than 
the first; it departs from directness in its use of the 
predicate (major term). In the third figure the same 
indirectness occurs ; the subject of the conclasion was 
not a subject in its premiss. But in the fourth figure 
the order is wholly inverted, the subject of the con- 
clusion had only been a predicate, whilst the predi- 
cate had been the leading subject in the premiss. 
Against this the mind rebels ; and we can ascertain 
that the conclusion is only the converse of the real 
one, by proposing to ourselves similar sets of prem- 
isses, to which we shall always find ourselves sup- 
plying a conclusion so arranged that the syllogism is 
in the first figure, with the second premiss first. 

§ 98. The unfigured Syllogism. 

A syllogism may be stated without making the 
terms either subjects or predicates ; so that it belongs 



LAWS OF THOUGHT. 20& 

to no figure.* Thus " since copperas and sulphate 
of iron are identical, and sulphate of iron and sul- 
phate of copper are not identical, it follows that cop- 
peras and sulphate of copper are not identical." 

§ 99. Modes of Syllogism. 

The mode of a given syllogism is the formal value 
of its three judgments as to their quantity, quality, 
and relation. It is expressed by the three letters 
that denote them (§ 76). These, with the addition 
of the number of the figure to which it belongs, con- 
vey the whole form of the syllogism; thus All, 
Fig. I. is known to mean 

All M is P 

/x Some S is M 

. • . Some S is P 

7 

I § 100. Table of all the Legitimate Modes in all 
I Figures. 

\ The following Table is an index of the modes in 
[>* which a good inference can be drawn.f It is ar- 
ranged according to the order in which the vowels 
occur in the alphabet, so that, when any mode has 
been omitted, as not available for inference, the eye 



* Sir IF. Hamilton. 

t It Avas drawn up by the Author, independently of all assistance 
from living authorities, in 1841, and published in 1842. Another 
Table is given below, with such additional modes as contain th» 
doubtful negative judgments n and o. 
14 



210 



OUTLINE OF THE 



can detect and supply it, and the mind examine the 
reason for its omission. 



Fig. I. 
AAA 


ElG. 11. 


I 
AA I 




A E E 




A II 


A 


All 


A U A 


AU Y 


AU A 


AY I 


A Y Y 


AY A 


E AE 


E AE 


EA 


E I 


E I 


E I 


E UE 


E UE 


EUE 


E Y 


E Y 


EYE 


I U I 

I Y I 

OUO 


I U I 

I Y I 


I A I 
I U I 

AO 
OUO 


YO 

U A A 


U A A 


UA Y 


TJ E E 


U E E 


UE E 


U II 


U I I 

U 


U I I 


U 0.... 




UUU 


UUU 


UUU 


U Y Y 


U Y Y 


U Y A 




Y A A 


YA Y 


Y EE 




YE E 


Y 


Y I I 

YU A 




YU Y 


YU Y 


Y Y Y 


Y Y I 





Fig. III. 



Some of these modes exemplify different special 
rules and theorems of logical writers, of which a few 
are subjoined. 



Pig. I. A A A and A A I are the only modes to which the dictum 
de omni directly applies — " Whatever is said of a class may be said 
of a contained part of the class." 



LAWS OF THOUGHT. 211 

Fig. I. A U A is a formula into which a " perfect induction " might 
fall, where we afl&im something of a whole class, because we have 
found it true of all the individuals or species which the class contains. 
Thus 

X 7 and z are P 

S = X y and z 
Therefore S is P 

Leibnitz gives the formula " Cui singula insimt, etiam ex ipsis con- 
st! tutum inest." 

Pig. I. E A E and E I are the only modes to which the dictum 
de nullo appUes. " What is denied of a class must be denied of any 
part of the class." 

E U E and U E E in all figures. " Si duorum quae sunt eadem 
inter se unum diversum sit a tertio, etiam alterum ab eo erit diver- 
sum." Leibnitz. 

Pig. I. and ii. U A A. " Quod inest uni coincidentium, etiam 
alteri inest." Leibnitz. 

M= P 

All S is M 

. • . All S is P 

U TJ U in all figures. " Quae sunt eadem uni tertio, eadem sunt 
inter se." 

§ 101. A Mode of Notation. 

To be able to represent to the eye by figures the 
relation which subsists in thought between concep- 
tions, tends so greatly to facilitate logical analysis, 
that many attempts have been made to attain it. Of 
two important schemes, that of Euler and that of 
Sir W. Hamilton, an account will be given hereafter. 
The scheme now to be explained is that which Lam- 
bert makes use of, in his Neues Organon. 

A distributed term is marked by a horizontal line, 
with the letter S, P, or M attached, to denote that it 
is the subject, predicate, or middle term of the syllo- 
gism. 

P 



212 OUTLINE OF THE 

An undistributed term is marked, not by a definite 
line, but by a row of dots, to show its indefiniteness, 
thus 

S 

These are the two forms of quantity in which sepa- 
rate conceptions may occur. But when two con- 
ceptions are joined in a judgment, another power 
as to quantity must be represented also. Let the 
judgment be, " All plants are organized," and let the 
lower line represent the subject and the upper the 
predicate ; will this representation convey the whole 
truth? 

P 

S 

In one point it is inadequate, that the term " organ- 
ized" is not wholly indefinite. We mean indeed 
by it, only some organized things ; but then one part 
of it is made definite by affirming it of plants. We 
do not know how many, or what, individuals, come 
into the conception " Some organized things " by 
itself; but when it occurs in this judgment, we are 
certain of some individuals in it, viz : those which are 
" all plants." This we are able to express by a line 
partly definite, partly undetermined, thus 



S 



Every affirmative judgment may be represented by a 
line drawn under another, the lower being always 
the subject. Negative judgments, which express 



LAWS OF THOUGHT. 213 

that one conception cannot be contained under an- 
other, are represented by two lines drawn apart from 
each other, the predicate being a little higher than 
the subject, thus — 

P 

S ^ . 

But in a syllogism there are three terms, so that we 
require three lines to represent their relations ; and 
the diagram thus drawn will supply some important 
illustrations of the nature of inference. Suppose the 
premisses are, " All matter undergoes change, and 
the diamond is a kind of matter," the relations of the 
three terms may be thus exhibited. 



M 

S . 



From this notation, besides the two premisses given, 

1. All M is P 

2. AU S is M 

we may, by reading downwards, gather that 

3. Some P is M, and 

4. Some M is S 

which are in fact immediate inferences by conver- 
sion from each of the premisses respectively. But 
^urther, from knowing that M stands under P, and 
S under M, we have learnt that S stands also under 



214 OUTLIXE OF THE 

P, and this we may express, leaving M altogether 
out of our statement, 

5. All S is P 

6. Some P is S 

the former being the proper conclusion from our 
premisses, and the latter the converse of the conclu- 
sion. 

Where one premiss is negative, and by the canon 
of syllogism one only can be of that quality, the no- 
tation will be 

P 

M 

S 

which would be read thus, 

NoMisP 

All S is M 
Therefore, No S is P. 

Finally, every universal judgment of substitution, 
or U, may be expressed by two equal lines 

P 

S 



But when such a judgment expresses a logical divis- 
ion, as " Organized beings are either plants, brutes, 
or men," the divided character of the predicate may 
be expressed by breaking up the line which icpre- 



sents it, thus 



P 

S 



LAWS OF THOUGHT. 215 

which would be read, " All S is either x y or z." 
The contrary process, of logical composition, which 
is used to express induction, as " Plants, brutes, and 
men are the only organized beings " would appear as 

P 

S X V z 



and be read " x y z make up the sum of P." — The 
reader will find great advantage in comprehending 
the rules of syllogism, from figuring the syllogisms 
to which they happen to apply, according to these 
directions. 



§ 102. Equivalent Syllogisms. 

Though the Reduction of Syllogisms, from a so- 
called imperfect, to the perfect, figure, is no longer 
requisite now that the power of the dictum de omni 
et nullo is confined to the proper limits, the relations 
of three conceptions can be expressed, commonly, in 
more than one syllogism of the same figure, and al- 
ways in difierent figures. And the advantage of any 
adequate system of notation is that it not only rep- 
resents to us the syllogism itself, which is one way 
of stating the mutual bearing of three conceptions, 
but, in making that mutual bearing visible, it furnishes 
the means of stating it in other syllogisms. An ex- 
ample will illustrate this. 

" No agent more effectually imitates the natural 
action of the nerves, in exciting the contractility of 
muscles, than Electricity transmitted along theii 
trunks, and it has been hence supposed, by some phi- 



216 OUTLINE or THE 

losophers, that electricity is the real agent by which 
the nerves act upon the muscles. But there are 
many objections to such a view ; and this very im- 
portant one among the rest, — that electricity may be 
transmitted along a nervous trunk vjhich has been 
compressed by a string' tied tightly round it, whilst the 
passage of ordinary nervous power is as completely 
checked by this process, as if the nerve had been di- 
vided." * This argument may be thrown into the 
following syllogism, as the most direct form of state- 
ment. 

Electricity will travel along a tied nerye. 
The nervous fluid will not travel along a tied nerve, 
.•. The nervous fluid is not electricity. 

This is a syllogism in the second figure, and of the 
mode A E E, which will be found in the Table in 
the preceding section, and is therefore a valid mode. 
The middle terra is the conception " able to travel 
along a tied nerve ; " and one of the other terms is 
under it, and the other not, so that they cannot agree ; 
and this mutual relation may be conceived by the 
following lines : — 

M 

P^ S 



The question now is — whether having obtained this 
relation, we cannot find other modes, besides A E E, 
Fig. II. in which to express it. 

As the physiologist is most engaged with the parts 
and functions of the animal economy, to him " The 
nervous fluid " would be the most prominent term, 
the subject of thought, and therefore would very 

* Carpenter, Animal Ph^'^siology, p. 437. 



LAWS OF THOUGHT. 217 

properly be the subject of the whole syllogism. But 
the same three conceptions would be the grounds for 
arguing — 

The nervous fluid win not trayel along a tied nerve, 
Electricity will travel along a tied nerve ; 
.". Electricity is not the nervous fluid. 

This is E A E, Fig. ii. which is also a valid mode ; 
and it would best suit one who was examining elec- 
tricity. It is the same as the last statement, except 
that the present is the converse of the former conclu- 
sion. Again, though somewhat less naturally, we 
may state it, 

Nothing that travels along a tied nerve can be the nervous fluid, 
Electricity travels along a tied nerve ; 
.•. Electricity cannot be the nervous fluid. 

This is E A E, of the first Figure. From what has 
been said we see that the relations between any three 
conceptions in our mind are permanent ; that the 
expression of them is not permanent, but may now 
assume one mode of syllogism, now another; that 
the conditions which determine us to one form as 
more natural than another are, partly, the difference 
of extension in the conceptions, where it is ascer- 
tainable, partly the greater prominence of one con- 
ception in our thoughts at the tirfie, which entitles 
it to be the subject ; that any one of the syllogisms 
founded on the conceptions is sufficient to ascertain 
their relations ; and that by a scheme of notation we 
may represent not merely one of the cognate syllo- 
gisms, but the ground of all of them, from which they 
3an afterwards be drawn out separately. 



218 OUTLINE OF THE 



§ 103. Sir W. Hamilton's Scheme of 3Iodes and 
Figures of Sijllogism. 

A mode of notation proposed by Sir William 
Hamilton is, beyond doubt, one of the most impor- 
tant contributions to pure Logic which has ever been 
made since the science was put forth ; and I am for- 
tunate in being permitted to annex it.* Its excellen- 
cies are — that it is very simple, that it shows the 
equivalent syllogisms in the different figures at a 
glance, that it shows as readily the convertible syllo- 
gisms in the same figure, that it enables us to read 
each syllogism with equal facility according to ex- 
tension and intension, the logical and the metaphys- 
ical whole. 

In this Table M denotes the middle term ; and 
C and r the two terms of the conclusion. A colon 
(:) annexed to a term denotes that it is distributed, 
and a comma (,) that it is undistributed. Where 
the middle term has a : on the right side, and a , 
on the left, we understand that it is distributed when 
it is coupled in a judgment with the term on the 
right, and undistributed when coupled with the 
other. 

The syllogisms actually represented are all affirm- 
atives, being twelve in each figure ; and the affirm- 
ative copula is the line -, the thick end denoting 

the subject, and the thin the predicate, of extension. 
Thus C : , M would signify " All C is (some) 

* It is also to be found in Mr. T. Spencer Dai/nes's New Analytic. 
t(^ But the order of the Moods is different, and tlie present order is thai 
finaUy fixed on by Sir W. H. 













N 




\ / 








1 


\ / 












\ / 






\ / 










\ / 


5 


I 


Zi 




1 




) 


- 


\/ 






-> 


\/ 








\/ 




r. 


\/ 






^ 


\/ 


•• 


.a 


^ dj 


g 


> 


.^- 




^ 


X 


^ 




^ 


X 


^ 




§ 


X 


s 


S 


Y 


^ 




g 


X 


^ 


•§ 


o ^ 




3 






•• 


A 








A 








A 






A 








A 




S 






















1 


























1 


•1 


-^ 


































' 




1 






1 


3 


H 


1 


















1 




















1 


£ 


O 


• • o r^ .. r> FN .. rv .. •• ..rs rv 


ca 


J? 


O 0,0 QO 00 QO 00 


.5: 


[±< 


f-i t-i Ph [LiPh P^hPh P-,Ph Phi:h f-^ 


-o 


o 




■§ 


H 


1 




































1 




1 






:3 . 


:^ 






































1 










g-| 


« 


1 








1 


























\ / 






1 








B a 




) 




) 




\/ 








\/ 








\/ 




^ 


\/ 


__ 






\/ 




ii 


o 


1 


\ 


g 


i 


§ 


X 


^ 




^ 


X 


s 




g 


X 


g 


^ 


X 


1 




^ 


X 


^ 


-g 


o 














































s .. 




1 










































- 


I 









- 


6' 


•i a 
1:1 

2 a 


w 


(L, (^ p^ ^hC^ P^fH fHfH (IhPh fH 


» 2* 


§ 


"^ "1 C 1 


•- 


1 f < 


•■ 


1 1 


^ 




^.2 


<1 




























a ^ 


J 


























X / 


t, a 


>-] 








I 


\ / ' 




\ / 




\ / 




\ / 




\ / 


J 




s 


1 ■ 


( ^ 


1 


^ 


x= 


^. 


x^ 


^ 


X- 


^ 


X" 




CO 




I 






1 


1 




1 










m 










I 




1 


1 




I 










I' 




rN 'N •• .N'-*^ ■• -'^ -^ 


§ 




6' q"00 QO 00 00 


1 




:s iS .S **' ■> -g' iS' -2 ^' 'S =g 


i 




'' ) 


:3 




' 


1 
..J 








L 





^ 























M 



LAWS OF THOUGHT. 219 

M." In reading off the intension, the thin end de- 
notes the subject. 

But from each affirmative can be formed two neg- 
ative syllogisms, by making each of the premisses 
negative in turn. The negation is expressed by 
drawing a perpendicular stroke through the affirm- 
ative copula ; thus ■ [ . In the negative modes 
the distribution of terms will remain exactly the 
same as it was in the affirmatives from which they 
were respectively formed. 

The line beneath the three terms is the copula of 
the conclusion ; and in the second and third figures, 
as there may be two conclusions indifferently, a line 
is also inserted above, to express the second of them. 

The mark v— >v-— ' under a mode denotes that 
when thie premisses are converted, the syllogism is 
stUl in the same mode. 

But a ^]^><:^ between two modes, signifies that 
when the premisses of either are converted, the syllo- 
gism passes into the other. 

The middle is said to be balanced when it is dis- 
tributed in both premisses alike. The extremes, or 
terms of the conclusion are balanced, when both alike 
are distributed ; unbalanced, when one is and the 
other is not. 

According to this scheme there are 12 affirmative 
Moods in each Figure, and 24 negatives, or 36 alto- 
gether. All the possible moods of syllogism are here 
exhibited ; but the value of the inference in some of 
them is so small that they would never actually be 
employed. For example, by making negative the 
first premiss of No. v. Fig. ii. we have such a syllo- 
gism as — 



220 OUTLINE OF THE 

Some stones do not resist the action of acids. 
Some metals resist the action of acids ; 
.•. Some metals are not sorne stones, — 

where there is undeniably an inference, but ofle 
which can scarcely be said to add to our knowledge 
of the subject of it. To facilitate a comparison of 
this Table with the former one (p. 210), its Moods 
are translated into equivalent letters ; and an exam- 
ination will prove that every mood not containing 
the vowel ,; or w * occurs in both tables, which after 
deducting the disputed moods so marked, coincide 
in all respects. 



§ 104. Euler^s System of Notation. 

Perhaps the most celebrated plan of notation is 
that which Euler has described in his Lettres a une 
princesse cf Allemagne.\ But, as it only represents 
the extension of the terms, and not the opposite ca- 
pacity, of intension, it is inferior to that which has 
just been described. The sphere of a conception is 
represented by a circle ; an affirmative judgment by 
one circle wholly or partly contained in another; 
and a negative by two separate circles. The judg- 

* The objections to the employment of the judgments denoted by 
this will be found in § 77, together vrith the grounds on which they 
have been defended.. See Sir W. Hamilton's Note in Mr. Bai/nes's 
New Analytic, p. 153, and Discussions in Philosophy, p. 614, by the 
same author, for further elucidations of this system. 

t Made known before Eider by Lange in his Nucleus Logicce Weisi' 
ance, 1712, and apparently first employed by Christ. Weise, who died 
in 1708. Ploucquet employed the square, and Maass the triangle ia- 
stead of the circle. Drobisch Logik. § 84. 



LAWS OF THOUGHT. 



22] 



Table of Modes. 



Fig. I. Pig. ii. Fig. hi. 

Aff. Neg. Aff. Neg. Aff. Neg. 



L 


U 


U 


U 


E U 


E 


u u u 


E U 


E 


U 


TJ 


u 


E TJ E 










U E 


E 






U E 


E 








TJ E E 


ii. 


A 


Y 


I 


V Y 
A 


0) 


Y Y 


I 


Y 
Y 


6) 
(J 


A 


A 


I 


71 A a 
A n (•> 


iii. 


A 


A 


A 


V A 
A V 


V 
V 


Y A 


A 


A 
Y V 


V 
V 


A 


Y 


A 


V Y V 
A 7? 


It. 


Y 


Y 


Y 


Y 
Y 






A Y 


Y 


V Y 
A 






Y 


A 


Y 


A 
Y 5? 


V. 


A 


I 


I 


V I 

A 6) 


0) 
0) 


Y I 


I 


I 

Y o> 




A 


I 


I 


5? I 0) 

A (J w 


vi. 


I 


Y 


I 


GJ Y 

I 


0) 


I Y 


I 


u Y 
I 


(J 


I 


A 


I 


u A (J 

1 T] u 


Tii. 


U 


Y 


Y 


E Y 
U 






U Y 


Y 


E Y 

U 






U 


A 


Y 


E A 
V n 


Till. 


A 


U 


A 


V U 
A E 


V 
V 


Y U 


A 


u 

Y E 


V 
V 


A 


U 


A 


V H V 
A E V 


ix. 


U 


A 


A 


E A 

U V 


E 


U A 


A 


E A 


E 
V 


TJ 


Y 


A 


EYE 

U J? 


X. 


Y 


U 


Y 


u 

Y E 



E 


A U 


Y 


V U 
A E 



E 


Y 


U 


Y 


U 

Y E E 


xi. 


TJ 


I 


I 


E I 

U 6) 





U I 


I 


E I 

U 6) 




(J 


U 


I 


I 


E I 

TJ 6J w 


xii. 


I 


TJ 


I 


E 

1 U 




I U 


I 


u U 
I E 


6) 
V 


I 


U 


I 


u J] u 
IE? 



Sum of all the valid Modes in each Figure. 



This Table. 



Former Tabla 



I. 36 (= 12 aff. + 24 neg.) — 14 weak neg. = 22 
II. 36 (== 12 aff. + 24 neg.) — 16 weak neg. = 20 
III. 36 (= 12 aff. + 24 neg.) — 16 weak neg. = 20 



^ 



222 OUTLINE OF THE 

ment that " All men are mortal " has the effect of 
including' men in the class of mortal beings, which 
would be represented by a small circle for " men," in 
a large one for " mortal." The annexed diagram ex- 
hibits (i) the Mood AAA, (ii) E A E, (in) All, 
and (iv) E I O, all of the first Figure.* 



§ 105. Inference in Intension, Extension, and 
Denojnination. 

That a judgment may be interpreted either in its 
extension, or intension, or denomination, has been 
already shown (§ 78). Every syllogism has the 
same property. Thus, 

All metals are lustrous, 
Iridium is a metal ; 
.". It is lustrous — 

may either be read in extension — 

The class of metals are some lustrous things, 
Iridium is in the class of metals ; 
.•. Iridium is among lustrous things — 

or in intension — 

The notion of some lustrous things attaches to the notion of all 

metals, 
The notion of some metal is implied in Iridium ; 
•. The notion of some lustrous thing attaches to that of Iridium — 

* The system of symbolical notation of Professor Boole, of Cork, 
ought not to be passed over. But it is so intimately connected with 
his whole work, "An Investigation, of the Laws of Thought," that an 
attempt to compress it into a paragraph would only do an injustica 
to a thoughtful and profound writer. 



LAWS OF THOUGHT. 



223 







224 OUTLINE OF THE 

or in less uncouth, but at the same time, less accu- 
rate form — 

Lustrousness belongs to our notion of metals, 

Being a metal is part of the notion of Iridium 

•. Lustrousness belongs to our notion of Iridium : 

or lastly, in denomination 

Metals may be called lustrous, 
Iridium has the name of metal ; 
.'. Iridium may be called lustrous. 

Although any argument may be so expressed as 
to give one or other capacity greater prominence, it 
is at all times possible to read an argument in any 
of the three powers, preserving of course the dis- 
,tribution of terms unchanged. The most important 
term in the extensive point of view is the least in 
the intensive, because it embraces most objects, but 
we know least of its nature ; in the example, " lus- 
trous " contains the other terms under it, and more, 
but "iridium" implies in it the notion of lustrous 
and much more ; " lustrous " therefore has the great- 
est extension, " iridium " the greatest intension. 
Where the terms are equal, as in U U U of all 
Figures, extension and intension are in cequilibrio. 



§ 106. Conditional 'tSytlogisms. 

A syllogism in which t^iefe is one pure conditional 
judgment or-more'^fsee § 71.) is called a Conditional 
Syllogism. All arguments of this class come into 
the scheme of syllogisms already given, when they 



LAAVS OF THOUGHT. 225 

are properly exhibited. " The principal forms are 
here annexed. 

I. In cases where M is N, C is D, 

In cases where A is B, M is N ; 

.*. In cases where A is B, C is D. 

II. In cases where C is D, M is N, 

In cases where A is B, M4s"^; ^ /^ -^.v^ A^-^ 
.'. In cases where A is B, 6-is-©^. C -^ ^^-^ J? 

III. In cases where M is N, C is D, 
In cases where M is N, A is B ; 
.•. In cases where A is B, C is D. 

These three forms are composed entirely of con- 
ditional propositions. They are in the three different 
figures; and examples of them will be correct or 
incorrect according as they do or do not conform 
to the principles of the syllogism already laid down 
as to affirmation and negation, distribution of terms 
&c. 

IV. In cases where M is N, C is D, 
But in the given cases M is N ; 
Therefore in these cases C is D. 

Y. In cases where M is N, G is not D, 

But in the given cases M is N ; 
Therefore in the given cases C is not D. 

VI. In all cases where M is N, and in no others, C is 1), 

In the given cases M is not N ; 
Therefore in the given cases C is not D. 

VII. In all cases where M is N, and in no others, C is D, 
In the given case C is D ; 
Therefore M is N, 

VIII. In all cases where A is B, M is N, 
In the given cases M is not N ; 
Therefore in the given cases A is not B 
16 



226 OUTLINE OF THE 

IX. In all the cases where A is B, M is not N, 
In the given cases M is N ; 
Therefore in the given cases A is not B. 

It may facilitate the use of these formulee if con- 
/crete examples of them are added, expressed in the 
[form of ordinary categorical syllogisms. 

(f^ I. (AAA. Fio. I.) 



All cases where law prevails, are cases where the rights of the 

weaker are secured, 
All well-ordered states exhibit such cases ; 
Therefore in all well-ordered states the rights of the weaker are 

secured. 

II. (AEE. Fig. II.) 

All cases where rain falls are cases where clouds obscure the sky, 
All cases of heavy dew are cases where there are no clouds ; 
Therefore cases of heavy dew are not cases of rain. 

III. (A A I. Fig. hi.) 

All cases of ignorance are cases in which a crime is excused. 
Such cases are instances of an absence of will or intent ; 
Therefore some cases of absence of will are cases in which crimei 
are excused. 

IV. (AAA. Fig. I.) 

The supposition that matter cannot move of itself implies the ex- 
istence of a higher moving power, 
What we adopt is the supposition, &c. ; 
Therefore we adopt the view that a higher moving power exists. 

V. (E AE. Fig. i.) 

The fact that the moon presents always the same face to the eartli 

implies that she has no diurnal revolution on her axis. 
But she does present the same face to the earth ; 
Therefore she cannot go through the diurnal revolution. 



LAWS OF THOUGHT. 227 

VI. (UEE. Fig. I.) 

All the times ■when the moon comes between the earth and the suH; 

are the sole cases of a solar eclipse, 
The 11th of February is not such a time ; 
Therefore the 11th of February "will exhibit no ecHpse of the sun. 

VII. (U A A. Fig. i.) 

All the times when the earth's shadow falls on the moon, are the 

sole cases of a lunar echpse, 
The 5th of June is such a time ; 
Therefore the 5th of June will be the occasion of an eclipse. 

VIII. (A E E. Fig. ii.) 

The case of the earth being of eqiial density throughout would imply 

its being 2| times as dense as water, 
But in fact, it is not 2^ times as dense as water, but 5|- times ; 
Therefore it is not of equal density. 

IX. (E A E. Fig. ii.) 

No cases of excessive dew are cases of cloudy night. 

But this night is cloudy ; 

Therefore the dew wiU not be excessive. 

Other modes might be added, but these may suf- 
fice to exhibit the nature of the conditional syllogism, 
together with its affinity to the regular forms. That 
peculiar connection between two facts which con- 
stitutes the one cause and the other effect, offers a 
problem worthy of the study of the metaphysician.* 

* The principal opinions upon the source of our idea of cause and 
effect may be thus sketched : — 

i. Locke refers this idea to sensation. We see that one thing has 
"the power to create, or generate, or make, or alter another thing, 
and such powers we call causing, and the things that have them are 
causes. Hum. Und. ii. 26, § 2. 

ii. Hume rejects the notion that the fact which we call a causa 



228 OUTLINE OF THE 

But that the two are connected, and that their re- 
exercises any power whatever over the effect. But from constantly 
observing the association or sequence of two facts, we begin to see 
their invariable connection, and to represent one as the cause of the 
other (Essays, vol. ii. p. 86.) A number of observations is thus a 
necessary condition of our forming this idea. But why do we give 
it a name that distinguishes it from sequence, if it is mere sequence ? 
The sunset always follows a flood tide, at a greater or less interval; 
but no one associates them imder the idea of causation. 

iii. Leibnitz assigns to every thing that exists a certain force or 
power, and thus constitutes it a cause. Existence, indeed, is measured 
by power. Whilst Locke, as Hume remarks, infeis causation from the 
fact that tilings come into being and are changed, Leibnitz regards 
power and causation as primary attributes of all being, not inferred 
from but implied by it. Nouveaux Essais, B. ii. 

iv. Kant considered the notion of cause and effect as one of the 
forms of the understanding, one of tlie conditions under which we 
must think. We are compelled by a law of our mind to arrange the 
impressions of our experience according to this form, making one 
thing a cause and another an effect; but whether there exists in the 
objects themselves that which we mean by a cause and an effect, we 
cannot determine. (Critique. Transcendental Analytic.) 

T. The view of Maine de Biran is chiefly known through the 
writings of Victor Cousin and others. According to him (and I 
quote through his critics only), the notion of cause originates with 
our consciousness of tlie power of will, which recognizes the will as 
the cause of our actions; and we transfer this personal power by a 
kind of analogy to all the operations of nature. 

vi. Sir William Hamilton traces the idea of causality to that limita- 
tion of our faculties wliich prevents us from realizing an absolute 
commencement or an absolute termination of being. When we think 
of a thing, we know that it has come into being as a phenomenon, 
but we are forced to believe that the elements and facts that produced 
the phenomenon existed already in another form. In the world to 
whicli our observations are confined, being does not beejin ; it only 
changes its manifestations ; the stock of forces (so to speak) is not 
augmented, though their direction and operations alter. By our 
idea of causation we express this belief; the causes of any tiling are 
the forces and elements of it, before they took shape in it. But see. 
an admirable Conspectus of the theories of Causality with a much 
fuller account of his own Yie\y in Sir If. H.'s Discussions, &c. 
p. 685,/oL 



LAWS OF THOUGHT. 229 

latioii resembles in many particulars that of subject 
and predicate in an ordinary proposition, is all that 
a logician need ascertain. An ordinary proposition 
asserts that the thought of one thing or attribute 
draws with it, or implies, the thought of another 
thing or attribute ; the conditional judgment de- 
clares that the thought of one fact brings with it the 
thought of another fact ; but whether the connection 
of the facts is such as to invest them with a partic- 
ular property, or arises only in the mind, and is one 
of the forms of thought under which the mind views 
external impressions, we shall not inquire. If the 
inferences in the categorical syllogism might be de- 
scribed by the principle Nota notce est nota rei ipsius 
(see § 93), the corresponding form of conditional 
syllogism would be explained by Effectus effecius 
est effectus causce. And so throughout might the 
parallel be traced between every categorical mode 
and a parallel hypothetical. 

One distinction of causes must not be forgotten, 
that which is between the cause of our knowing a 
fact {causa cog-noscendi), and the cause of the fact's 
existence {causa essendi). When we say " the 
ground is wet, because it has rained," we assign to 
the rain the latter character ; it is the cause of the 
ground actually being in this state. But the cause 
may change places with the eifect ; " it has rained 
because the ground is wet " — where the wetness of 
the ground is the cause of our being sure there has 
been rain, and this is all that we mean to assert, 
and not the absurd proposition that the wetness 
which followed, could bring about the rain which 
preceded. The inquiry into causes which occupies 



230 OUTLINE OF TUh 

the inductive philosopher applies to causes of things 
being, and not properly to causes of our knowing 
things. 



§ 107. Disjunctive Syllogisms. 

An argument in which there is a disjunctive judg- 
ment (§ 71) is called a disjunctive syllogism. A 
pure disjunctive argument (i. e. one in which no im- 
mediate inference has to be supplied) may be at 
once referred to its proper mode, by ascertaining the 
quantity and quality of the disjunctive judgment 
in it. The principal forms of such syllogisms are 
annexed. 

1. (In A U A. Fig. i.) 

C D and E are P, 
All S is either C D or E ; 
.-.All Sis P. 

2. (In E U E. Fig. i.) 

Neither C nor D nor E is P, 
All S is either C or D or E ; 
. • . S is not P. 

3. (In U E E. Fig. ii.) 

All P is either C or D or E, 
S is neither C nor D nor E ; 
. • . S is not P. 

4. (In E U E. Fig. ii.) 

P is neither C nor D nor E, 
S is either C or D or E ; 
. • . S is not P. 



V 



LAWS OF THOUGHT. 231 

5. (In I A I. Fig. III.) 
Either A B or C is P,* 
A B and C are S . 

. \ . Some S is P. 

6. (In A U A. Fig. iii.) 
C D and E are B, 
C D and E — A ; 

. • . A is B. 

Concrete examples of these forms are— 

1. Solid, fluid, and aeriform bodies are elastic. 
Every body is solid, fluid, or aeriform ; 
Therefore every body is elastic. 

2. Neither England, Ireland, Scotland, nor Wales is unhealthy, 

All Great Britain is either England, Ireland, Scotland, or Wales ; 
Therefore Great Britain is not unhealthy. 

3. A science is either a pure, inductive, or mixed science, 
Astrology is none of these ; 

Therefore Astrology is not a science. 

4. A question neither affirms nor denies, 
A judgment must affirm or deny; 
Therefore a judgment cannot be a question. 

5. Either Christianity or Judaism or Mohammedanism is the true 

religion, 

Christianity, Judaism, and Mohammedanism are alike mono- 
theistic ; 

Therefore a monotheistic religion is the true one. 

* This is really a particular affirmative judgment (I) ; for it 
means that " Some of A B C are P." It must not be confounded 
with itsf apparent converse. " P is either A B or C," which is a 
universal substitutive judgment (U) and means that P is divisible 
into A B and C. Thus " a primitive colour must be blue, red, or 
yellow " is converted into " blue, red, and yellow are the primitive 
colours," and not into " either blue, red, or yellow is a primitive 
colour." 



232 OUTLINE OF THE 

6. Oxygen, hydrogen, chlorine, &c. are lighter than water, 
Oxygen, hydrogen, chlorine, &c. are the whole of the gases ; 
Therefore all the gases are Mghter than water.* 



The complex disjunctives are founded upon the 
law of distinct division akeady stated (§ 107). ^f 
a genus is divided into so many species, what is iu 
one of the species cannot be in another. In bringing 
them into the form of common syllogisms, we need 
only employ a new premiss, gained by an immediate 
inference under this very principle. Thus — 

AU A is B or C, 

This A is not B; 
. • . This A is C— 



would become 



[All A is B or C, therefore] 
All (A that is not B) is C, 
This is an (A that is not B) 
This is C. 



All sciences are either pure, inductive, or mixed sciences. 
Astronomy is not a pure or inductive science ; 
.*. It is a mixed science — 

v/ould stand as a syllogism in AAA. Fig. i. 

Sciences that are not pure nor inductive are mixed. 
Astronomy is a science not pure nor inductive ; 
Therefore it is a mixed science. 

* This is the formula for the Induction hy simple Enumeration, 
where on finding a property to belong to every member of a class 
singly, we infer that it belongs to the whole class. The worth ol 
Buch an argument is considered below. 



LAWS OF THOUGHT. 233 

§ 108. Complex Syllogism. Sorites. 

The simple syllogism is the type of all reasoning, 
and the test to which all reasoning may be brought. 
But there are more complex forms of argument, not 
less natural than the syllogism itself, which do not 
require to be reduced to syllogisms to show their 
correctness, just as we know ice to be ice without 
reducing it to the needle-shaped crystals with which 
freezing commences. Of this kind is the Sorites. 

Three or more premisses in which the predicate of 
each is the subject of the next, with a conclusion 
formed from the first subject and last predicate of 
the premisses, have been called a Sorites, or accumu- 
lating argument, from the Greek word uupd?, a heap. 
The name is not very appropriate ; the German title 
of chain-argument [kettenschluss) expresses better the 
nature of a process in which the mind goes on from 
link to link in its reasoning, without thinking it ne- 
cessary to draw out the conclusions as it passes. 
"Where the premisses are all universal affirmative 
attributive judgments, not the least* confusion can 
arise from thus postponing till the end the realization 
of the results. But where the premisses are judg- 
ments of different kinds, the reasoning is more diffi- 
cult to follow, and it may be necessary to draw out 
each syllogism separately, in order to see whether it 
is in a valid mood, and, if otherwise, what is the 
fault in it. This is done as follows : — 

All the premisses but the first are leading-premisses 
of so many distinct syllogisms; therefore there are 
as many syllogisms, minus one, as the Sorites has 
premisses. For the second premiss of the first syllo* 



234 OUTLINE OF THE 

gism the first judgment of the Sorites must be taken 
whilst to each succeeding one the conclusion of ita 
predecessor must be the second premiss. A diagram 
will make this much clearer. 

1. A is B, 

2. B is C, 

3. C is D, 

4. D is E, 
Therefore A is E. 

Reduced to 

I. II. II. 

2. B is C, 3. C is D, 4. D is E. 

1. AisB, [A is C], [A is D], 

[.-. AisC], [.-.AisD] [.-.AisE.] 

These syllogisms are all in A A A. Fig. i. a valid 
mode. An invalid mode occurring before the last 
syllogism would not only be wrong itself, but, as 
furnishing a premiss to its successors, would vitiate 
every syllogism that follows. 

The number of conclusions which these premisses 
admit of, is greater than actually appears. We may 
conclude A C, A D, A E (which appear) ; and B D 
B E, C E. Five premisses instead of four would 
increase the number of conclusions to ten.* There is 
a form of the Sorites to which the name of Goclenius 
its inventor has been attached, which is the same as 

* Cora. Arist. Pri. An. i. 25. The formula for ascertaining tho 
number of conclusions is this : — 

Let the number of premisses = n, the number of terms = n -|- 1 ' 
then the number of conclusions = n (n — 1) 



LAWS OF THOUGHT. 235 

the common form, except that the premisses are re- 
versed. It would run 

Dis E, 
C is D, 
Bis C, 
AisB, 
.-. A is E. 

In the Goclenian Sorites extension is made more 
prominent, by starting with the premiss which has the 
two widest terms ; in the common form intension 
predominates, as the narrower terms precede. The 
former descends in extension from the predicate of 
the conclusion ; the latter ascends in intension, from 
the subject. The Goclenian form suits deduction 
best ; the common or Aristotelian form, induction. 
The Goclenian descends from law to fact ; the com- 
mon ascends from fact to law.* 

This will be clearer from a pair of examples. 

* A " pretty quarrel " long existed amongst logicians, which of the 
two was to be called proqressive and which regressive. TiU Kant's time, 
the Goclenian was called progressive, the common regressive. Kant 
reversed it, followed by Kiesewetter and others. Jacob reversed it 
again, followed by Krug and others. Troxler ii. 100. It was a mere 
strife about words. If we are discovering truth by the inductive 
method, the Aristotelian form is progressive ; if we are teaching 
truth, or trying our laws upon new facts, we use deduction, and the 
Goclenian form is progressive. In an apt but familiar figure — if I am 
on the ground floor, and wish to fetch something that is above, my 
going up stairs is my progress towards ray object, and my coming 
down is a regression ; if the positions of myself and the thing are re- 
versed, going down would be progi-ess, and returning up, regress. 
The inductive trutli-seeker is on the ground-floor of facts, and goea 
up to seek a law ; the deductive teacher is on a higher story, and cai- 
ries his law down with him to the facts. 



236 



OUTLINE OF THE 



'{ 



( 



GOCt-ENlAN OR BESCEXDING 
SORITES. 



f'- 



Sentient beings seek happiness, 
All finite beings are sentient, 
All men are finite beings, 
Cains is' a man ; 
Therefore he seeks happiness. 



AKISTOTELIAN OR ASCEXDINQ 
SORITES. 

Caius is a man, 
All men are finite beings, 
All finite beings are sentient. 
All sentient beings seek happi- 
ness ; 
Therefore Caius seeks happiness. 



In the following example a mixed order prevails : — 



(^ 



That ■which thinks is active. 
That which is active has strength, 
That which has strength is substance. 
The soul thinks ; 
Therefore it is substance. 



The premisses of the Sorites may be, all or some 
of them, hypothetical ; indeed as this argument is 
Dut an aggregation of simple syllogisms, the rules 
for the construction of simple syllogisms apply to 
its several parts ; with this one caution, that in the 
Sorites each foregoing syllogism furnishes a premiss, 
not expressed, to the next succeeding one, and there- 
fore we must see not only that each is good in itself, 
but that it will furnish an available premiss to its 
successor. This may be tried by altering one of the 
higher premisses in any of the examples into a nega- 
tive ; at the next step, an error will be apparent. 

4 

§ 109. The Dilemma. 

The Dilemma is a complex argument, partaking 
both of the conditional and disjunctive. It is a syllo- 
gism with a conditional premiss, in which either the 
antecedent or consequent is disjunctive. It may prove 
a negative or an affirmative conclusion ; in the 



LAWS OF THOUGHT. 237 

former case it is said to be in the mt)de of rem oval 
{modus tollens), because it removes or refutes some 
conclusion that has been proposed for proof : in the 
latter it is in the mode of position [modus ponens)y 
because the proposed question is laid down as proved. 
The following forms of it, with the manner in which 
they are presented as syllogisms, may be sufficient. 

I. 
If A is B or E is F, then C is D, 
But either A is B or E is E ; 
.-. C is D. 

II. 
If A is B, then C is D or E is E, 
But neither C is D nor E is E ; 
.'. A is not B. 

III. 
If some A is B, either the m that are A or the n that are A, are B, 
But neither the m that are A nor the n that are A are B ; 
.'. A is not B. 

The same regarded as simple syUpgisms. 

I. 
[The cases of A being B and E being E] are [cases of C being D], 
This is [a case of A being B or E being E] . 
.*. Tliis is [a case of C being D]. 

II. 
[The case of A being B] is [a case of C being D or E being E].. 
This is not [a case of C being D or E being E] ; 
.'. This is not [a case of A being Bj. 

III. 
Neither m of A nor n of A are B, 
All A is either m or n ; 
.-. No A is B. 

The word Dilemma means " double proposition," 
60 that the whole argument takes its name from the 
one mixed judgment in it. When this is more than 
double, as in " If a prisoner is legally discharged. 



238 OUTLINE OF THE 

either the magistrate must refuse to commit, or the 
grand jury ignore the bill, or the common jury acquit, 
or the crown exercise the prerogative of pardon," 
the argument has been called a Trilemma, Tetra- 
lemma, or Polylemma, according to the number of 
members the judgment may have. 

The following are concrete examples of the for- 
mulae. 

I. If the king is moved or if he is covered, I am checkmated the 
next move ; One or the other must be ; Therefore I shall be check- 
mated. 

II. If a man cannot make progress towards perfection, he must 
either be a brute or a divinity ; But no man is either; Therefore 
every man is capable of such progress. 

III. If some science can furnish a criterion of truth, either a formal 
or a real science must do so ; But (for different reasons) neither the 
formal sciences nor the real do so ; Therefore science affords no cri- 
terion of truth. 

Tkilemsia. If the system of the universe is not the best possible, 
we must suppose either that the Creator willed not a better one, or 
that he knew no better one, or tliat he could not create a better. 
The tirst cannot be true (it is against His goodness). The second 
cannot be true (it assails His wisdom). The third cannot be true 
'it limits His power). Therefore the system of the universe is the 
best. 



The popular notion of a Dilemma, that it is a 
choice of alternatives, each of them fatal to the 
cause or the character of an adversary, is coun- 
tenanced by many logicians, but can have no place 
in pure Logic, into which the object to be gained 
by arguments, or the personal consequences which 
follow from admitting them, ought not to enter, and 
the properties of the arguments themselves are the 
sole object of consideration. 

If the criminal knew the consequences of his act, he was wicked ; 
if he did not know the consequences, he was insane. 



LAWS OF THOUGHT. 239 

This is really two distinct hypothetical judgments, 
associated because they happen to have a common 
term — " the criminal ; " and because one or othei 
of them must be true ; and two distinct syllogisms 
would be founded upon them, as the counsel for the 
defence would probably take for his second premiss 
— " He did not know the consequences of his act, 
therefore he is insane," while the counsel for the pros- 
ecution would maintain that " He did know the con- 
sequences, and therefore was guilty." No doubt it 
is a great detriment to a prisoner to be found either 
guilty or insane, but this does not appear upon the 
face of the argument, and therefore pure Logic does 
not take it into account. A new judgment would be 
required to show the connection of the two notions ; 
so that besides the two conditional syllogisms, con- 
tained in the argument itself, a third is tacitly ad- 
mitted, that shows the connection of the other two. 
This sort of argument, a great favourite with the 
Sophists and old logicians, is called also Si/llog'ismus 
Crocodilinus, and Syllogismus Cornutus ; and "the 
horns of a dilemma " are known even to common 
language. 

§ 110. Incomplete Syllogisms. 

The arguments used in thinking, speaking, or 
writing, are never drawn out in strict technical form, 
except by practised logicians, desirous of exhibiting 
their art to those who, like themselves, are conver- 
sant with it. A sentence which contains the mate- 
rials of a syllogism, not technically expressed, has 
been called an enthymerae, or an enthymematic sen.» 



240 OUTLINE OF THE 

tence. Aristotle understands by enthymeme a syllo- 
gism such as would be used in rhetoric where the 
full and orderly expression of premisses and conclu- 
sion would seem laboured and artificial. And as the 
omission of one of the premisses is a common, per- 
haps the commonest, feature of enthymeraes, logi- 
cians have defined them as syllogisms with one 
premiss suppressed. But we may also omit the con- 
clusion, or invert the order of premisses and conclu- 
sion ; and unless we extend the name enthymeme to 
these cases we put a considerable restriction upon its 
original meaning. Let the enthymeme then be de- 
fined — an argument in the form in which it would 
naturally occur in thought or speech. 

§ 111. Prosyllogism and Episyllogism. 

In a chain of reasoning, one of the premisses of 
the main argument may be the conclusion of another 
argument, in that case called a prosyllogism ; or the 
conclusion of the main argument may be a premiss 
to a supplementary one, which is called an episyl- 
logism. Let us take the syllogism which a coroner's 
jury might have to go through. The question is, 
" Has A. B. been poisoned ? " and the syllogism is, 
" A man who has taken a large quantity of arsenic 
has been poisoned, and A. B. is found to have done 
so, therefore he has been poisoned ; " with the addi- 
tion of a prosyllogism and episyllogism the reasoning 
would run — "A man who has taken arsenic has 
been poisoned ; and A. B. has taken arsenic, for the 
application of Marsh's and Reinsch's tests discover 
it (Prosyl.) ; therefore A. B. has been poisoned and 



LAWS OF THOUGHT. 241 

therefore we cannot return a verdict of death from 
natural causes." (Episyl.) A prosyllogism then is a 
syllogism whose conclusion is a premiss in a given syl- 
logism ; an Episyllogism is one, ivhose premiss is a 
conclusion in a given syllogism. The Sorites, Pro- 
syllogism and Episyllogism, deserve our attention as 
the joints of thinking by which the various members, 
the acts of immediate and mediate inference, are knit 
together in an organic connection. Of them, how- 
ever, the first can rarely be employed ; the two last 
meet us continually. 



..OUTLINE 



LAWS OF THOUGHT. 



PAST IV. 

APPLIED LOqiC. 

" Mais, paroe que I'esprit se laisse qulequcfois abuser par de faussea 
lueurs, lorsqu'il n'y apporte pas I'attention necessaire, et qu'il y a 
bien des choses que I'on ne connait que par un long et difficile exa • 
men, il est certain qu'il serait utile d'avoir des regies pour s'y con- 
duire de telle sorte, que la recherche de la verite en fut et plus facile 
et plus sure ; et ces regies, sans doute, ne sent pas impossibles."— 
Aknauld. 



APPLIED LOGIC. 




§ 112. Province of Applied Logic. 

N the foregoing pages the Laws of 
Thought have been considered solely in 
themselves; and their connection with 
the objects they belong to has been 



studiously kept out of view. It has been shown 
that every conception consists of marks, without any 
attempt to explain how the marks are to be obtained ; 
that a judgment of a given quantity, quality, and re- 
lation, can be converted or opposed, no matter whether 
it is a true judgment with reference to the matter it 
sets forth ; that a given form of syllogism is correct 
and its proof cogent, whether or no the premisses it 
draws from are frivolous, or even incorrect. In order 
to understand aright the laws of thinking in them- 
selves, this procedure was necessary ; for we must 
distinguish betw^een faults in the forms themselves, 
which we have the means of correcting without 
travelling beyond them, and faults in the materials 
of thinking, that cannot be corrected without a ref- 
erence to the objects that supplied them. For ex- 
ample, " some men are infallible," is a judgment cor- 
rect in form, but false in matter, as our knowledge 
of humanity teaches us ; again, to convert " some 
men are philosophers," into " all philosophers are 



246 OUTLINE OF THE 

men," is wrong in form, although it happens that 
the latter judgment, erroneously produced, is male- 
rialiy correct. 

Applied Logic teaches the application of the forms 
of thinking to those objects about which men do 
think These objects arrange themselves under three 
grea"t divisions, Man, the Universe, and Absolute 
Being. When the views we take of objects are 
substantially correct, when our thoughts correspond 
with facts, we are said to be in possession of the 
truth ; and thus we return to a definition of Applied 
Logic already proposed. It is the science of the 
necessary laws of thought as employed in attaining 
truth. 

§ 113. Science. 

These laws may be applied to the fragmentary 
knowledge and scattered information gathered by 
every one in his passage through the world ; they are 
unconsciously applied in this way every instant. But 
it would be a higher application of them to erect by 
their means a complete structure of the truth that 
related to one object or set of objects, as Zoology 
contains all that relates to animals. Geology all we 
know of the earth's structure, and Psychology aU that 
pertains to the human mind and soul. Such a sys- 
tem of the truths that relate to one set of objects is 
called a science, which has been defined (p. 26), a 
system of principles and deductions, to explain some 
object-matter. To fulfil its intention every science 
must have attained to ti'ue statements concerning its 
object-matter, so far as the nature of the case and 
the present means of examination allow ; it must bo 



LAWS OF THOUGHT. 247 

able to define the object-matter, and its several sub- 
ordinate parts, with clearness and precision ; and it 
must be able to indicate the extent of the domain 
the object-matter covers ; and lastly it must exhibit 
these results in a systematic and harmonious shape. 
For the first it must employ Induction and Deduc- 
tion ; the second is the province of Definition ; the 
third is provided for by Division ; and the fourth may 
be referred to Method. 



§ 114. Is a Philosophic Criterion of Truth possible. 

The search after truth cannot long dispense with 
any one of these instruments ; and even with the 
free use of them, the history of science shows how 
slow has been the advance, how largely (to use Leib- 
nitz's image) the sand and mud of error have been 
mixed with the gold grains of truth. All of them 
in their degree have to do with evidence, with the 
proof of propositions ; Induction and Deduction 
chiefly with the discovery and appreciation of evi- 
dence, and Definition and Division chiefly with the 
statement and arrangement of its results. Hence, if 
we have to answer the question whether a Criterion 
of Truth, i. e. a standard for judging of the truth of 
propositions, is possible,* we answer that evidence 

* Plato speaks of " Experience, prudence, and reason," as affording 
conjointly a Kpt-rjpiov of truth (Pol. 582 A.). This for the sense of 
the word. Tor other proposed criteria, not mentioned in the text, 
we have that of Wolff, determinabUitas prcedicati per notionem subje.cti 
(but it applies only to explicative judgments — see p. 175) ; that of 
Descartes, " that is true which is clearly known and perceived," but 
he admits that the test is somewhat vague ; and lastly that of Plato, 
" truth is conformity Avith the ideas." Evidence is used by the Carte- 
sians, sometimes in the sense of evidentness ; but we employ it ta 
mean "the grounds which make evident." 



248 OUTLINE OF THE 

is the sole means of establishing, and therefore the 
sole standard for testing, the truth of any propo- 
sition, and that all the operations connected with 
evidence contribute their share to the criterion. But 
such a maxim as that " a judgment must rest upon 
sufficient evidence " is too abstract to be of use by 
itself as a test of truth. In fact no shorter rule, no 
more portable touchstone can be indicated, for the 
examination of objective truth, than the whole sci- 
ence and rules of evidence. And in the special 
cases where other criteria appear to be applied, as in 
the discussion whether religious truth is to be tried 
by external testimony or internal conviction, whether 
historical evidence or the religious sentiment is the 
best criterion, the dispute is only as to the kind of 
evidence that shall take precedence. 
V Four principal criteria of truth have been in dif- 
ferent forms advocated by logicians ; the reader is 
now in a position to estimate their value. 

1st Criterion. The principle of Contradiction. 
" The same attribute cannot be at the same time 
affirmed and denied of the same subject" Or "the 
same subject cannot have two contradictory attri- 
butes." Or " the attribute cannot be contradictory 
of the subject." * To illustrate this — at a particular 
time facts were observed as to the motions of the 
planets, which were inconsistent with the received 
theory that these motions were circular. The theory 
was consequently modified, first by the introduction 
of epicycles, and finally by the substitution of the 

* The first mode of statement is Aristotle's, to yup avTo afxa vnaf^ 
X-'iv re Koi fjjj indpxecv udvvarov rw avTu ko?. Kara to avTO. Metaph. IV 
'>r ) lii. The second is Aristotelian ; the third is Kant's. 



LAWS OF THOUGHT. 249 

theory of elliptic )-evolution ; because otherwise the 
astronomer must have affirmed of the planets a cir- 
cular and a non-circular motion, or in other words 
must have assigned to a subject, to which he had 
already given " circular motion," a predicate contra- 
dictory of this. 

2d Criterion. The principle of Identity. " Con- 
ceptions which agree can be united in thought, or 
affiirmed of the same subject at the same time." 
This principle is the complement of the former. 

3d Criterion. The principle of the Middle being 
excluded (lex excJusi medii). " Either a given judg- 
ment must be true, or its contradictory ; there is no 
middle course."* So that the proof of a judgment 
forces us to abandon its contradictory entirely, as 
would the disproof of it force us upon a full accept- 
ance of the contradictory. This law, among other 
uses, applies to the dialectical contrivance known to 
logicians as reductio per impossibile. 

4th Criterion. The principle of svfficient (or 
determinant^^ reason. " Whatever exists, or is true, 
must have a sufficient reason why the thing or prop- 
osition should be as it is and not otherwise." J 
From this law are educed such applications as 

* This is the uvTl&eaic ^f ovk can jiera^v Ka-^' avrrjv, of Aristotle, 
(An. Post, I. i. Kad^' avr^v, " as appears per se from the nature of the 
assertion." Trend.) Compare Metaph. IV. (T.) 7, and Alexander's 
comment. 

t C. A. Crusius, in a tract on this subject, finds faxilt with the 
ambiguity of "sufficient," whicli might seem "sufficient for this 
effect" witliout excluding it from the possibihty of producing some 
other. According to liim, tliis principle involves absolute necessity, 
and destroys morality. 

J Leibnitz, Theod. I. § 44. Upon this principle, and tliose o/ 
Contradiction and Identity, Leibnitz has based his Logic. 



250 OUTLINE OF THE 

these : — 1. Granting the reason, we must grant what 
foiiows from it. On this depends syllogistic infer- 
ence. 2. If we reject the consequent, we must 
reject the reason. If we admit the consequent, we 
do not of necessity admit the reason. 

Now the distinction between formal and material 
truth, or in other words between self-consistency in 
thinking, and conformity with facts, assists materi- 
ally in forming an estimate of the worth of these 
principles. A judgment may be formally true, and 
materially false ; as in the inference " No men err, 
Socrates is a man, therefore he cannot err," which is 
correctly drawn, yet proves a falsehood from a false- 
hood : or it may be materially true, yet formally 
false, as, " Socrates is a man, Socrates erred, there- 
fore aU men err; " where a true judgment has been 
drawn from two true judgments, yet not correctly. 
The four criteria in question are useful in securing 
formal truth, that is, in keeping our thoughts in 
harmony with each other; but for the discovery of 
material truth, for giving us thoughts that are true 
representations of facts, they are either useless, or 
only useful as principles subordinate to the higher 
criterion of which all applied Logic is but the ex- 
pansion, that every proposition must rest upon suffi- 
cient evidence. The principle of contradiction has 
been already implied in the doctrine of privative 
conceptions in the theory of disjunctive judgments 
and inferences and in other places. The principle 
of the excluded middle is the canon of the inference 
from contradictory opposition upon which the refuta- 
tion of a false conclusion must rest. The principle 
of the sufficient reason is implied in the syllogistic 



LAWS OF THOUGHT. 251 

canon that every conclusion must follow from and 
depend on sufficient premisses ; it is employed in 
other forms, in hypothetical reasonings in particular. 
And in these purely formal applications the criteria 
have their importance, but that not the highest. 

Viewed as instruments for judging of material 
truth, they sink into mere rules for the reception of 
evidence. The first is a caution against receiving 
into our notion of a subject any attribute that is 
irreconcilable with some other, already proved upon 
evidence we cannot doubt. The second is a per- 
mission to receive attributes that are not thus 
mutually opposed, or a hint to seek for such only. 
The third would compel us to reconsider the evi- 
dence of any proposition, when other evidence 
threatened to compel us to accept its contradictory. 
The fourth commands that we seek the causes and 
laws that have determined the existence of our sub- 
ject, for the subject cannot be adequately known 
except in these. So that the vaunted criteria of 
truth are rules of evidence ; and there is no one 
means of judging of truth, except what the whole 
science of Evidence affords. 

A.. Construction of Science. 

§ 113. Induction and Deduction. 
Induction* is usually defined to be the process of 

* Opinions are somewhat divided both as to the meaning ol 
i-Kayuyi], the word of which Induction is the English equivalent, 
and the nature of the argument that bears the name. i. It is sup- 
posed to be a persuasive argument to which a person is induced 



252 OUTLINE OF THE 

drawing a general law from a sufficient number of 
particular cases ; Deduction is the converse process, 
of proving that some property belongs to a particular 
case, from the consideration that it comes under a 
general law. More concisely. Induction is the pro- 
cess of discovering laws from facts, and causes from 
effects ; and Deduction that of deriving facts from 
laws, and effects from their causes. E. g-., that all 
bodies tend to fall towards the earth is a truth 
which has been obtained by considering a number 
of bodies where that tendency has been displayed, 
by induction ; if from this general principle we argue 
that the stone we throw from our hands will show 
the same tendency, we deduce. If it were always 
possible duly to examine the whole of the cases to 

(eTtaysTai) to assent. Comp. UpoasxE f^V i^f riTTTjari to Ttpoar]veg avrov 
Kol 7/6v Kal kirayuyov [Epictetus, Ench. 84), where the last word 
means persuasive, alluring. Compare Cicero (de Inv. I. 31.). "Induc- 
tio est oratio, quas rebus non dubiis capiat assensiones ejus quicum 
instituta est; quibus assensionibus facit, ut ilU dubia quaedarn res, 
propter similitudinem earum rerum, quibus assentit, probetur." 2. 
It is the bringing in (to enayeiv) examples or comparisons, To ev tH^ 
eluovag E'iTa.vea-&ai, — {X.enophon, QScon. 17, § 15.) This latter deriva- 
tion finds most favour. Then the process itself is sometimes 
described as if it were a way of proving particular unknown facts 
from particular known facts. " Cum plura interrogasset [Socrates], 
quse fateri adversario necesse esset, novissime id de quo qu£erebatur, 
inferebat, cui simile concessisset." [Quinctilian, V. 11.) The logi- 
cian will see that this comes close to the logical Argument from 
Example. Both in Induction and Example, however, there is an 
appeal to a general law, expressed or implied. Our definition is 
i\\?it oi Aristotle (Top. I. 12.), "Induction is the process from par- 
ticulars to universals." In using the phrase " the syllogism from 
induction," A. hints at that wider \ie\Y of syllogism, as the simple 
element of all reasoning whatever, Avhich it is one main object oi 
this book to develop. See Heyder, Darstellung, pp. 60, 219 ; Evnesti, 
Lex. Techn. ; Trendelenburg, E:^cerpta, § 20 ; but cliiefly Eeinhardi 
Opuscula, I. 212. 



LAWS OF THOUGHT. 253 

which a law applies, and to see by intuition the 
pignificant and important parts of each, the process 
of Induction would be simple enough. But a com- 
plete inspection of all the cases is very seldom pos- 
sible ; even the laws on whose invariable operation 
the strongest reliance is placed, must have been laid 
down upon the evidence of a number of cases very 
limited when compared with the whole ; that men 
must all die, and that heavy bodies tend to fall 
towards the earth, are statements which no one can 
boast of having verified by enumeration. The per- 
fect certainty with which they are believed, rests 
upon far less than the millionth part of the cases 
that might be brought to bear witness about them. 
Nor again are the significant and essential circum- 
stances easy to observe, in the few cases that lie 
within the reach. Either they escape notice alto- 
gether, as did the fact of the earth's revolution in 
the early days of Astronomy ; or they are so en- 
tangled or overlaid with a mass of other facts that 
their importance does not at first appear, like the 
action of cold in the production of dew, before Dr. 
Wells's observations, or the influence of an open 
drain in producing and sustaining fever, till within 
the last few years. It appears then that the pure 
inductive syllogism, that argument by which a law 
is laid down as the exact sum of all the single cases, 
will not sufiice for scientific research. To take an 
example — 

Gold, silver, copper and the rest will combine with oxygen, 
Gold, silver, copper and the rest are the only metals ; 
Therefore all metals combine with oxygen. 

(A syllogism in A U A, Eig. iii. p. 227.) 



254t OUTLINE OF THE 

This argument could not be formed until people 
discovered what at first no one suspected, that oxy- 
gen was the cause of the rusting and tarnishing of 
metals ; and it still stands open to dispute if a metal 
should be hereafter discovered that refuses to com- 
bine with oxygen. Yet it might be selected as one 
of the inductions that approach most near to perfect 
enumeration. The logic of science then must em- 
ploy other instruments than this syllogism, so very 
limited in its application, so very liable to question. 
Four principal questions require to be answered by 
Applied Logic. 

1. How are the causes of facts to be distinguished, amidst a multi- 
tude of other facts, all open to observation 1 

2. How are causes discovered M'liich are less open to observation 
than the effects 1 

3. Wlien should an incomplete enumeration (or induction) of tacts 
be deemed sufficient, and on what principle 1 

4. How should new laws be expressed and recorded 1 

The following sections contain an indication of 
the answers to these four inquiries, but by no means 
a full exposition of them. 



§ 114. Search for Causes. Inductive Methods. 

All men are apt to notice likenesses in the facts 
that come before them, and to group similar facts 
together. The similarities are sometimes so obvious 
that the most careless observer is an-ested by them ; 
the rise of the tide to-day and yesterday, the tenden- 
cy to fall which a stone from the hand, an acorn from 
an oak, and a hailstone from a cloud exhibit alike, 
and the power of growth exhibited by a grain of corn 



LAWS OF THOUGHT. 255 

and a tulip root, afford g-roups of cases which seem 
so to classify themselves as to leave the mind little 
room for inquiry. The faculty by which such 
similarities are apprehended is called observation ; the 
act of grouping them together under a general state- 
ment, as when we say " All seeds grow — all bodies 
fall," has been already described as generalization. 

Now if any obvious generalization be examined, 
as for example " bodies tend to fall," we see that this 
only furnishes us with the sum of several distinct 
facts ; that " bodies fall " is only a shorter form of 
stating that this body falls, and that body, and that 
other, and so on till every single body has been men- 
tioned. Why all bodies tend to fall has not been 
stated. In other words a law has been laid down ; 
but the cause of its operation remains to be ascer- 
tained. A law or rule is a general principle em- 
bodying a class of facts ; when it is regarded in its 
connection with theory it usually has the former 
name, and when it is concerned with practice, the 
latter. The formation of such general propositions 
is the first procedure in the formation of science ; at 
the same time they are of little service unless accom- 
panied by the ascertainment of causes. 

What then do we understand by the cause of any 
given fact or thing ? We mean the sum of the facts 
or things to which it owes its being. We know that 
the various phenomena that engage us are not so 
many beginnings or new creations, but are parts of 
a long sequence of events, brought about by many 
facts that have passed already, and destined in their 
turn to bring about other phenomena. In this se- 
quence, no new force is gained or lost ; there is com' 



256 OUTLINE OF THE 

mutation of forces, but, so far at least as we can see, 
neither increase nor diminution. When we inquire 
into causes, we are only seeking one step higher up 
in the sequence for the forces now combined in the 
new phenomenon under examination ; we wish to 
know what concurring agencies they were, which 
brought this fact about. Now the older writers 
attempted not merely to find out these antecedent 
phenomena, but to assign the kind of share which 
each took in producing the result, by dividing causes 
into efficient, formal, material, concomitant, and the 
like. This is partly founded on a viTong view of 
causation, and it is partly beyond our reach. If we 
attempt with them to pronounce that the producing 
or efficient cause of any thing {causa principalis, 
Kiipiov alnov) is to be sought in one particular ante- 
cedent fact, whilst the other facts whose concurrence 
was no less required for the result, must take subor- 
dinate places as instrumental or impelling causes, 
we are in danger of the double mistake of elevating 
almost into a personal agent one of our phenomena, 
and of slighting others which have equally conduced 
to the end. All we know for certain is, that there 
are certain antecedents, the want of any one of which 
would have made the phenomenon wholly, or in its 
present shape, impossible. We must therefore apply 
universally, what the scholastic writers admitted in 
some cases, the principle that all the facts or ele- 
ments from which a new fact or thing draws its 
existence, i. e. aU the associate causes [causce essen- 
tialiter sociatce) of it, make up what we term its 
cause, on the scholastic maxim that " several partial 
causes concurring for one effect, must be regarded as 



LAWS OF THOUGHT. 257 

one " (causce partiales in toto concursu stant pro una). 
The cause of an explosion of coal-gas is not the 
lighted candle alone, nor the gas which it kindles, 
nor the admixture of common air which makes the 
gas explosive, but it is the concurrence of all three, 
/y The cause of any phenomenon is only then truly 
assigned when account has been taken of all the 
precedent phenomena. It remains to observe that 
common language is not always framed upon this 
complete view. If 1 shake an apple-tree and an 
apple fall, I am spoken of as the cause of the fall ; 
yet all that I did was to give an opportunity for the 
law of gravitation to act. In fact my action is 
selected as the cause, where a little thought would 
have shown that several causes concurred. This arises 
partly from the obvious sequence, in point of time, of 
the fall to my action. But although we say that the 
cause is antecedent to its effect, we must not under- 
stand this as implying invariable antecedence in 
point of time. The vices of the court and govern- 
ment concurred to cause the French Revolution, and 
were antecedent to it in time ; the law of gravitation 
causes the fall of the apple, and the oscillations of a 
pendulum, but it is not antecedent to these in point 
of time, but actually present in them. The antece- 
dence of the cause is one of relation, rather than of 
time ; if it were otherwise, that act alone which 
preceded in time a given phenomenon must be 
reckoned as its cause, where perhaps it only gave 
the occasion for the chief and constant cause to 
operate. He who applied the match to the powder 
would be the one cause of all the destruction tha^ 
followed the explosion of the mine. 

17 



258 OUTLINE OF THE 

Where it is proposed to inquire for the cause of a 
phenomenon, it is not implied that one cause can 
have determined it alone ; but that, most of the con- 
ditions being known, one unknown fact has had a 
great influence upon the result, and that our search 
is therefore confined to this. 

The principal rules which regulate, consciously or 
not, the search after the cause, are as follows : — 

1. The cause (or causes) must be sought among 
the invariable concomitants of the effect. 

But it must not be forgotten that the same effect 
may follow from causes entirely different ; as ebul- 
lition from the escape of steam and the disengage- 
ment of carbonic acid. In order to reduce our search 
to a single cause, we must narrow down our descrip- 
tion of the effect, so as to exclude similar, but not 
identical phenomena. 

2. The cause cannot be any thing which is present 
in other cases where the given effect is not produced, 
T;inless the presence of some counteracting cause shall 
appear, to account for its non-production. 

3. The cause is generally suggested by analogy or 
resemblance, from cases in which the connection of a 
cause and an effect is better known. 

4. The cause is frequently indicated by a variation 
of degree corresponding to a variation of the degree 
of effect. 

5. The cause will be more likely to appear from 
considering as many forms of the effect as possible. 

6. A suspected cause may be tested by allowing it 
to operate in circumstances of less complication, to 
see whether the effect is produced. 

7. Where complications exist, the eifects must he 



LAWS OF THOUGHT. 259 

narrowly estimated, to determine whether the causes 
discovered or suspected account for the whole of 
them ; if there is any residual effect, even in the form 
of a modification of the effects of the known causes,' 
we must seek for its cause also.* 

A few examples may be given in illustration. The 
Danish astronomer Romer was engaged in a course 
of observations on the revolution of one of the moons 
of Jupiter, in order to determine its precise time by 
observing the intervals between its eclipses. He as- 
sumed that the interval between any two disappear- 
ances of the satellite in the shadow of its planet, 
would give the precise time of its revolution. But 
in order to secure the greatest accuracy he continued 
the observations through several months. Had there 
been nothing to qualify the assumption, one observa- 
tion, free from error, would have enabled the astron- 
omer to predict the times of all the future eclipses of 
the satellite. But Romer found that his predictions 
were invariably wrong ; the observed time was later 
than the predicted time, and it was not long before 
he perceived that the error in this direction gradually 
and regularly increased. By and by he found a de- 
crease in the amount of difference between fact and 
calculation set in, as gradual and regular as the in- 
crease had been ; until at length the two became co- 
incident. Now, here was a phenomenon of which 
the cause was to be discovered. There was one fact 
which, Roraer well knew, accompanied the phenome- 
non, and varied with it in degree ; and that was the 

* In drawing up these rules I have derived much aid from Sir J. 
Herschel's Preliminary Discourse on Natural Philosophy, a work 
vrliich every student would do well to read carefully. 



260 OUTLINE OF THE 

change of the position of the earth in her orbit, and 
consequently a change in the distance of the earth 
from Jupiter. It was difficult not to associate these 
phenomena together, even before the causal connec- 
tion of one with the other was perceived. But E,o- 
mer was able to suggest the mode of their correction. 
The apparent retardation of the eclipse was not a 
retardation of the satellite itself, but of his perception 
of it. The light took time to travel ; and the differ- 
ence of the time of the eclipse, when seen from one 
part of the earth's orbit, nearest to Jupiter, and its 
time when seen from another part, most distant, 
would be exactly the time which .Ijght took to travel 
across a distance equal to the diameter of the earth's 
orbit. But this distance being known, E.omer was 
able to determine the velocity of light ; although it 
formed no part of his purpose in commencing the 
observations. 

It might be difficult to find a better example of 
the search after causes. Here the corresponding 
variations of degree of two phenomena distinctly 
indicated their connection ; this variation was a 
residual phenomenon, not at all expected in the out- 
set, and one which a perfunctory observer might 
have passed over as insignificant, or set down as the 
result of some error of his own. The need of 
embracing as many forms of a phenomenon as pos- 
sible in our observations also becomes indirectly 
apparent. It would be most difficult to measure the 
velocity of light upon the surface of our own planet, 
because that velocity is so great, not less than 
192,000 miles in a single second. But by including 
a set of observations where the distances are vast, 



LAWS OF THOUGHT. 261 

the calculation becomes comparatively easy ; for 
even at this almost incredible speed, the last beam of 
the satellite as it became extinguished in the shadow, 
took 16 minutes and 26 seconds to traverse the inter- 
val of space which came into the observations. 

The third rule, obvious as it is, has much influence 
on the progress of philosophy, according as it is well 
or ill observed. That the laws of nature are through- 
out uniform and harmonious, will be insisted on 
below; and science sees, as yet at least, no limits 
to the application of this maxim, for the relations 
between forces, which were hitherto considered quite 
distinct, if not opposed, are daily becoming more 
evident to observant eyes.* Hence there is no more 
abundant source of scientific improvement than the 
process of extending the causes of known phenomena 
to explain the unknown. " Galileo opened the path 
of all true astronomy, by the simple maxim that the 
same laws of motion which hold good on the sur- 
face of the earth, apply also throughout the celestial 
spaces ; and Lyell did the same thing for geology, 
by maintaining that the analogy of real and existing 
ought to be extended through all the immeasurable 
periods of past time."f The extension of the theory 
of types, ah'eady accepted in physiology, to chemis- 
try also, is probably opening out great results for that 
science. 

Under the sixth rule are included all the varieties 
of experiments, and of simplified observations. We 
are sure that the pitch of different musical tones 
depends on the number of vibrations of the air in 

* See Grove's Correlation of Physical Forces. 
+ Professor Powell's Unity of Worlds 



262 OUTI.IXK OF THE 

each, when in the instrument called the Sirene, we 
cause the vibrations and find that the proper musical 
note results. We know that the theory of double 
vision is correct, when in Wheatstone's stereoscope 
the eyes do actually receive the impression, even 
exaggerated, of a solid body, from two plain pic- 
tures taken from different points, as Ihe two eyes 
would see them. That the column of mercury in 
the Torricellian tube was counterpoised by a column 
of air, was proved by Pascal when he caused the 
instrument to be carried up the mountain, and 
found that as the ascent gradually diminished the 
height of the column of air above it, so was the 
column of mercury it was able to sustain, dimin- 
ished in proportion. Dr. Buckland was confirmed in 
his surmise that certain bones, bruised and mangled, 
were the relics of the prey of hyenas, when a liv- 
ing beast of the same species reduced before his 
eyes the bones of an ox to a condition precisely sim- 
ilar. 

In Sir Humphry Davy's experiments upon the 
decomposition of water by galvanism, it was found 
that besides the two components of water, oxygen 
and hydrogen, an acid and an alkali were developed 
at the two opposite poles of the machine. As the 
theory of the analysis of water did not give reason 
to expect these products, they were a residual phe- 
nomenon^ the cause of which was still to be found. 
Some chemists thought that electricity had the 
power of producing these substances of itself; and 
if their erroneous conjecture had been adopted, suc- 
ceeding researches would have gone upon a false 
scent, considering galvanic electricity as a producing 



LAWS 01- THOUGHT. 263 

rather than a decomposing force. The happier in- 
sight of Davy conjectured that there might be some 
hidden cause of this portion of the effect ; the 
glass vessel containing the water might suffer partial 
decomposition, or some foreign matter might be 
mingled with the water, and the acid and alkali be 
disengaged from it, so that the water would have no 
share in their production. Assuming this he pro- 
ceeded to try whether the total removal of the cause 
would destroy the effect, or at least the diminution 
of it cause a corresponding change in the amount of 
effect produced. By the substitution of gold vessels 
for the glass without any change in the effect, he at 
once determined that the glass was not the cause. 
Employing distilled water he found a marked dimi- 
nution of the quantity of acid and alkali evolved ; 
still there was enough to show that the cause, what- 
ever it was, was still in operation. Impurity of the 
water then w^as not the sole, but a concurrent cause. 
He now conceived that the perspiration from the 
hands touching the instruments might affect the 
ease, as it would contain common salt, and an acid 
and an alkali would result from its decomposition 
under the agency of electricity. By carefully avoid- 
ing such contact, he reduced the quantity of the 
products still further, until no more than slight traces 
of them were perceptible. What remained of the 
effect might be traceable to impurities of the atmos- 
phere, decomposed by contact with the electrical 
apparatus. An experiment determined this ; the 
machine was placed under an exhausted receiver, 
and when thus secured from atmospheric influence, 
•,t no longer evolved the acid and the alkali. 



2G4 OLiLINE OF THE 

A formal analysis of these beautiful experiments 
will illustrate the method of applying the rules of 
pure Logic in other cases. 

I. Statement of the case, the residual cause being still undiscovered. 
" The decomposition of "water by electricity produces oxygen ai-l 

hydrogen, with an acid and an alkali." 

II. Separation of the residual from the principal cause. 

a. " The decomposition of water produces oxygen and hydrogen. 

b. " Tlie production of an acid and an alkali in the decomposition 

of water may be caused by action on tlie glass vessel containing 
the water." (Problematical Judgment — A.) 

III. The latter Judgment — b — disproved by a syllogism in Mood E 

A O, Fig. III. with a conclusion that contradicts it. 
" A case in which I employ a vessel of gold cannot involve any 

decomposing action on a glass vessel, 
"A case in which I employ a gold vessel still gives the acid and 

the alkali ; 
" Therefore cases of the production of the acid and alkali are not 

always cases in which glass is decomposed.^' 

IV. Another attempt to suggest the residual cause. 

" The acid and alkali are produced by the decomposition of impu- 
rities in the water employed." 

Syllogism in A A I, Fig. iii. tending to prove this. 

" An experiment with distilled water must admit less impurity, 

" An experiment with distilled water gives less acid and alkali ; 

" Therefore sometimes with less impurity we have less acid and 
alkali." 

V. " The contact of moist hands " may be an additional cause of the 

residual phenomenon. 
Improved syllogism in A A I, Fig. iii. to include tlus concurrent 

cause. 
" An experiment with distilled water, and apparatus kept from 

contact of hands will admit still less impurity, 
" An experiment, &c. results in the production of still less acid 

and alkali ; 
" Therefore sometimes with still less impurity we have still less 

acid and alkali." 



LAWS OF THOUGHT. 265 

VI. Amended syllogism. AAA, Kg. iii. 

" A case ■where we use these precautions m vacuo is a case of no 
impurity, 

" A case where we use, &c. in vacuo is a case of no acid and al- 
kali ; 

" Therefore a case of no impurity is a case of no acid and alkali." 

VII. Immediate inference from last conclusion. 

" Cases of no-impurity are cases of non-production of acid and 
alkaK, 

" Therefore " (according to the example in p. 186, Division 11. of 
inference from A) 

" All cases of production of acid and alkali are cases of some im- 
purity ; " 

which was to be proved. 

An example like this brings into a strong light 
many of the characteristics of inductive reasoning 
Forms usually considered to be deductive are here 
freely employed. The later steps tend to confirm 
the earlier, on which, however, they themselves de- 
pend ; so that a mutual confirmation is obtained from 
setting them together. When the chemist substi- 
tuted gold vessels for the glass, and inferred from the 
continuance of the effect under this change that the 
glass could have nothing to do with its production, it 
was formally possible in the then state of knowledge 
that the glass might be the cause in the one experi- 
ment, and the decomposition of the gold in the other. 
But the later steps, which showed that the effect 
varied with the variations in a circumstance wholly 
distinct from the decomposition of glass or gold re- 
duced the possibility of maintaining such a view to 
the very lowest amount. Even the premisses of par- 
ticular syllogisms in the chain are sometimes tested 
and corrected by the conclusion, although formally 
the conclusion should entirely depend upon the prem- 



266 OUTLINE OF THE 

isses. The experimenter expected to find that the 
use of distilled water would exclude all impurity ; 
and he intended that his premiss (See No. IV.) should 
assert as much ; but when it turned out in the con- 
clusion that the supposed products of the impurity 
were still present, he was reduced to the choice be- 
tween abandoning that cause and recasting his 
premiss so as to admit that the cause was still pres- 
ent — " the use of distilled water gives less impurity.'* 



§ 115. Anticipation. 

The next question to be answered is — how are 
causes discovered which are not obvious, even after 
repeated inspections of the facts in which they lie 
hid ? By a power or combination of powers granted 
only to a few, which has been called Anticipation. 
It is the power of penetrating into the secrets of na- 
ture, before the evidence is unfolded ; it is enjoyed, 
as one might expect, by those only who have long and 
deeply studied the laws of nature already laid open, 
but not by all of these. It is no mere power of 
guessing, but an active imagination, supplied with 
materials by a clear understanding carefully disci- 
plined. The system of anatomy which has immor- 
talized the name of Oken, is the consequence of a 
flash of anticipation which glanced through his mind 
when he picked up, in a chance walk, the skull of a 
deer, bleached and disintegrated by the weather, and 
exclaimed after a glance, " It is part of a vertebral 
column ! " When Newton saw the apple fall, the 
anticipatory question flashed into his mind, " Why 
do not the heavenly bodies fall like this apple ? " lo 



LAWS OF THOUGHT. 267 

neither case had accident any important share ; New- 
ton and Oken were both prepared by the deepest 
previous study to seize upon the unimportant fact 
offered to them, and show how important it might 
become ; and if the apple and the deer's skull had 
been wanting, some other falling body, or some other 
skull, would have touched the string so ready to vi- 
brate. But in each case there was a great step of 
anticipation ; Oken thought he saw the type of the 
whole skeleton in the single vertebra and its mod- 
ifications, whilst Newton conceived at once that the 
whole universe was full of bodies tending to fall; 
two truths that can scarcely be said to be contained 
in the little occurrences in connection with which 
they were first suggested. 

The discovery of Goethe, which did for the vege- 
table kingdom what Oken's did for the animal, that 
the parts of a plant are to be regarded as metamor- 
phosed leaves, is an apparent exception to the ne- 
cessity of discipline for invention, since it was the 
discovery of a poet in a region to which he seemed 
to have paid no especial or laborious attention. 
But Goethe was himself most anxious to rest the 
basis of this discovery upon his observation rather 
than his imagination, and doubtless with good rea- 
son.* 

A mistaken notion prevails that this rapid antici- 

* Whewell's Hist. Sci. Ind. III. 477. As with other great dis- 
coveries, hints had been given already, though not pursued, both of 
Goethe's and Oken's principles. Goethe left his to be followed up 
by others, and but for his great fame, perhaps his name would never 
have been connected with it. Oken had amassed all the materials 
necessary for the estabhshment of his theory ; he was able at once 
to discover and conquer the new country. 



268 OUTLINE OF THE 

pation does not belong to the philosophic cast of 
mind — that it is precisely what Bacon condemns as 
the method which " hurries on rapidly from the par- 
ticulars supplied by the senses to the most general 
axioms, and from them as principles, and their sup- 
posed indisputable truth, derives and discovers the 
intermediate axioms." It is thought that caution, 
and deliberate examination of every particular we 
can find, before we allow ourselves to form any con- 
clusion whatever, are the conditions of all sound 
physical inquiry. There is here a confusion of two 
distinct things. Scrupulous caution should be ex- 
ercised before an hypothesis is considered to be 
proved; and the law that we believe to be true 
should be applied to every fact where it can be 
supposed to operate, and to every other law with 
which it might interfere, in order to verify exactly 
what was at first only a happy conjecture. Bacon 
meant to complain that this sober process did not 
always follow the bright thought and brilliant sug- 
gestion ; and perhaps that the bright thought itself 
was not suggested in the region of facts but in that 
of words. When the ancient Astronomy, rushing to 
the general axiom that " the circular motion is the 
most perfect," deduced from it the intermediate 
axiom that the motion of the heavenly bodies must 
be the circular, it might be reasonably charged with 
undue use of anticipation ; because the highest 
axiom, having no precise and definable meaning, 
cannot have really sprung from the contemplation 
of any facts, nor do it and the axiom drawn from 
it square with the facts they pretend to embrace. 
Where these conditions are obeyed, Anticipation is^ 



LAWS OF THOUGHT. ■ 269 

as it has been called, the mother of science. " To 
try wrong guesses," says Dr. Whewell, "is, with 
most persons, the only way to hit upon right ones. 
The character of the trae philosopher is, not that 
he never conjectures hazardously, but that his con- 
jectures are clearly conceived, and brought into 
rigid contact with facts. He sees and compares 
distinctly the ideas and the things ; — the relation 
of his notions to each other and to phenomena. 
Under these conditions, it is not only excusable, 
but necessary for him, to snatch at every semblance 
of general rule, — to try all promising forms of sim- 
plicity and symmetry." Anticipation then is the 
power whereby the mind presages a truth before it 
is fairly proved, before she makes the attempt to 
establish it by exact and cautious methods. Philos- 
ophy proceeds upon a system of credit ; if she never 
advanced beyond her tangible capital, her wealth 
would not be so enormous as it is. She works with 
a principle as true before she knows it to be so, 
because in watching how it operates upon facts 
consists the best means of establishing its truth; 
but she must be prepared at the same time to 
abandon and dismiss it whenever it is found to be 
in direct and irreconcilable conflict with established 
facts. 

§ 116. Inductive Conception, Colligation, Definition. 

Upon the nature of the Conception which Antici- 
pation furnishes, and its share in the formation of 
science, much conti'oversy ha& been raised, one party 
maintaining that the mind must be content with 



270 OUTLINE OF THE 

recording the facts, and another, that a Conception 
must anticipate the facts, and furnish us with a key 
to their language. Granting on the one hand that 
a theory or conception to explain facts will be worth- 
less, unless it shall prove to be itself a fact, we must 
admit on the other that great steps of inductive dis- 
covery are made with the help of a preconception, 
and not by merely throwing observations together. 
" That the fact of the elliptical motion of the planet 
Mars," says Dr. Whewell, " was not merely the sum 
of the different observations, is plain firom this, that 
other persons, and Kepler himself before his dis- 
covery, did not find it by adding together the obser- 
vations. The fact of the elliptical orbit was not the 
sum of the observations merely ; it was the sum of 
the observations, seen under a new point of view, 
which point of view Kepler's mind supplied." 

Such a conception, of which several instances 
have now been given, effects the Colligation (to 
borrow Dr. Whewell's name) of the facts to be ex- 
plained. But in order to connect itself with the 
facts, the conception itself must be capable of Expli- 
cation or Definition, not indeed of adequate defini- 
tion, since we shall have to alter our description of 
it from time to time with the advance of knowledge, 
but still capable of a precise and clear explanation. 
For example, a large class of facts is bound together 
by the notion of " chemical affinity," and could not 
be understood and arranged without the thread of 
this Conception to run through them. To refer 
them to this, their proper Conception, is one opera- 
tion ; to give a proper Explanation of chemical 
affinity another. 



LAWS OF THOUGHT. 271 

DisriNiTiON. — Chemical affinity is the power by which tlie particles 
of one elementary body are made to cohere with those of 
another, so as to produce a new substance, with characters 
either distinct from or opposed to those of the constituents 
separately. 

Pkoposition. — The tarnishing of metals, the neutral salts, &c. &c. 
are instances of the action of chemical affinity. 

Therefore we expect to find in them the characters mentioned in the 
definition. 

This is a syllogism in U A A, Fig. i. ; and whilst 
our reasoning faculty can draw it out and appreciate 
its truth and applicability, reason alone could not 
have suggested the premisses. No rules can be 
given for the discovery of the appropriate conception 
that explains our facts ; " such events," says Dr. 
Whewell, " appear to result from a peculiar sagacity 
and felicity of mind — never without labour — never 
without preparation ; yet with no constant depend- 
ence upon preparation, upon labour, or even entirely 
upon personal endowments." The suggestion of the 
conception may be due almost entirely to accident; 
the explication of it, often by far the more difficult 
step, cannot be accidental, but will proceed from a 
natural sagacity highly disciplined by scientific pur- 
suits. 

Conceptions not wholly correct may serve for a 
time for the Colligation of Facts, and may guide 
us in researches which shall end in a more exact 
Colligation. The theory of circular motions of the 
heavenly bodies was of this kind ; and in its turn 
the conception of epicycles. The theory of Phlogis- 
ton in chemistry made many facts intelligible , before 
the correcter one of Oxidation superseded it. So 
with the theory of " Nature abhors a vacuum," which 



272 OUTLINE OF THE 

served to bring together many cognate facts, not pre- 
viously considered as related. Any incorrect concep- 
tion of this kind has a place in science, whilst and in 
so far as it is applicable to facts and renders them 
intelligible. As soon as facts occur which it is in- 
adequate to explain, we either correct, or replace it 
by a new one. 

§ 117. Complete and Incomplete Induction. 

The third question that demanded an answer was 
— on what principle are incomplete inductions, i. e. 
examinations of facts that stop short of complete 
enumeration, sufficient to establish general laws ? 
The answer will contain the most interesting and 
important of the principles of Logic. All our expe- 
rience teaches us that in the universe, the " Cosmos," 
whose very name means order, regularity and uni 
formity prevail, and caprice and uncertainty are ex- 
cluded. Whilst it is conceivable that any one of the 
natural laws in which we place most confidence 
might be reversed, while it is certain that many of 
them have been miraculously suspended for pm-poses 
proportionably great and important, our present be- 
lief in their permanence is almost unlimited. The 
thought that there might be no more daylight, if our 
planet ceased to revolve whilst one side of it was 
averted from the sun — ^that a draught from the spring 
would to-day destroy the life which it recruited yes- 
terday — ^that a stone thrown from the hand would 
remain suspended in mid-air instead of falling — 
never enters our minds, except perhaps as an amus- 
ing fancy; yet each of these things is formally pos« 



LAAVS OF THOUGHT. 273 

sible. Our confidence in the uniformity of natural 
laws is embodied in the Canon, that under the same 
circumstances and with the same substances the same 
effects always result from the same causes. This great 
inductive principle is itself proved by induction, and 
partakes of the same formal defect that may be 
charged against other inductive results, viz : that its 
terms are wider than our experience can warrant. 
Many groups of facts, connected as causes and 
effects, have not been examined ; and in them it is 
conceivable at least that there may be capricious 
causes producing opposite effects at different times. 
If this were otherwise — if the canon were the result 
of a simple enumeration of all possible cases, its pres- 
ent value as a rule would disappear ; since it is to 
unknown and unexamined cases that we chiefly wish 
to apply it. We draw a universal canon from an 
experience less than universal, and then employ it 
to justify us in drawing other universal truths from 
other particular experiences. 
/ The difficulty, however, in applying this Canon is 
to discover the existence of a law of nature in any 
set of facts, and how far the interference of other 
laws permits it to operate. And here the relation 
between Deduction and Induction, between Syn- 
thesis and Analysis, is of great service. These pairs 
of terms correspond exactly, as names for the same 
two processes ; but Induction and Deduction give 
prominence to the law. Analysis and Synthesis to 
the fact. Thus we call the law of gravitation an 
inductive law, and speak of deductions irom it, 
thinking more in both cases of the universal than 
of the particular cases it referred to. But we ana 

18 



274 oinijNr: of 'iiii': 

lyze a fact or a substance, and make a synthesis 
(or placing together of elements) to reproduce the 
fact or substance. Using the two former names, 
the universal, the law, the world of conception, the 
abstract is made prominent ; using the two latter, 
we give promiruence to the single case, the phenom- 
enon, the world of the senses, the concrete. The 
supposed general principle may be tried by applying 
it to a new particular case ; the analysis of a fact 
into its elements may be tested by putting the ele- 
ments together anew, and seeing if the fact is repro- 
duced ; the correctness of the observations may be 
confirmed by careful experiment. And such attempts 
offer a twofold advantage. If, on applying some 
general principle of which we are still uncertain, to a 
new particular case, we find that it helps to explain 
the particular, this is one fruit of the process ; and 
another is that our confidence in the general principle 
is materially strengthened. Law explains fact ; fact 
confirms law. And after this alternate ascent and 
descent has been a few times performed, our belief 
in the correctness of its results is quite complete. 

This process can be understood most readily from 
examples. The metal called Potassium was discov- 
ered in acting on potash by the voltaic battery ; and 
thus far the two judgments — 

Potash is an alkali. 
Potash yields Potassium — 

would seem sufficient to describe the result. But 
not so ; a mind disciplined to scientific inquiry saw 
at once that this single fact was an indication of a 
law. In the system of nature is no caprice ; if the 



LAVfS OF THOUGHT. 275 

power of yielding a metal belonged to this alkali 
as such, beyond doubt other alkalies would partici- 
pate in it. These two judgments therefore become 
premisses to an act of inductive reasoning. 

(AAA, Fig. HI.) 

Potash yields a metal, 

Potash is an alkali ; 

Therefore all alkalies contain a metal. 

Now this syllogism is formally incorrect; for we 
cannot argue from a single alliali to the whole, and 
the property we have discovered may belong to this 
alone in connection with some undiscovered pecu- 
liarity. How shall this be ascertained ? By trying 
how the conclusion, upon which suspicion rests, will 
apply to new cases ; by experimenting on another 
alkali, as if the universal law were already established, 
by deducing from it, as we have induced to it. 

(A A A, Fig. I.) 

All alkalies contain a metal. 

Soda is an alkali ; 

Therefore it must contain a metal. 

The experiment is tried, and answers perfectly 
And the success of the prediction operates strongly 
to raise our belief in the conclusion on which it pro- 
ceeded. That alkalies in general have a metallic 
base was indicated at first by one case alone, that of 
potash ; but the chemist was guided by that case to a 
second attempt, and now a second one strengthens 
his belief that a law exists. To extend the trials to 
the alkaline earths, is suggested by their similarity to 



276 OUTLINE OF THE 

alkalies ; with them too the experiments are success- 
ful, and the law is considered to be established. And 
though ammonia furnishes an apparent exception, as 
it has been found impossible from the volatile nature 
of that substance to procure ammonium from it, I 
suppose that no skilful chemist doubts that ammo- 
nium exists, so strong is the general conviction that 
nature's laws are uniform, and that where most sub- 
stances alike in their general character, exhibit some 
striking property, it has been granted to them all 
without exception. 

Two principles then are established, that the cor- 
rectness of synthesis is proportionate to that of the 
preceding analysis ; and that a doubtful analysis may 
be confirmed by a synthesis. In other words, a cor- 
rect induction furnishes the premiss for a sound de- 
duction, and a doubtful induction must be verified 
by deductions from it. Examples of these may be 
found on every side. The artilleryman, when he 
points a gun according to known rules, executes a 
synthesis of several principles, the law of gravitation, 
that of momentum, that of atmospheric resistance ; 
if his shot misses, it wiU be either because some ele- 
ment has been left out of the analysis, the compar- 
ative force perhaps of different sorts of powder, and 
the windage of a loose ball in the ban-el of the piece ; 
or because the influence of each of the known laws 
has not been duly apportioned. The theory that 
marble is carbonate of lime fused under pressure has 
been made highly probable by the (synthetic) experi- 
ments of Bir James Hall, who made a substance 
closely resembling marble by those means. A correct 
analysis of lapis lazuli was suspected to be erroneous, 



LAWS OF THOUGHT. 277 

because there seemed to be nothing in the elements 
assigned it, which were silica, alumina, soda, sulphur, 
and a trace of iron, to account for the brilliant blue 
colour of the stone ; accidental synthesis, which was 
followed up by intentional, reproduced it, and thus 
the analysis was found to be correct, whilst the syn- 
thesis is now daily performed for commercial pur- 
poses. The law that the planets are retained in their 
orbits by an attractive force that varies inversely as 
the square of their distance from the sun has been 
worked out to its theoretical results, and these have 
been compared, synthetically, with the known facts. 
Theory was found not to correspond with fact in all 
respects, and thus it became necessary to revise the 
analysis, and discover the residual causes that pro- 
duced the variation ; which astronomers have suc- 
ceeded in doing. 

By the mutual cooperatien then of these two pro- 
cesses, the physical sciences are advanced.* If no 
attempts were made to draw a conclusion and see 
what use could be made of it, till grounds formally 
complete were before us, conclusions would never t a 
drawn. The certainties by which the chemist, tl » 

* Table of the relation of these processes. 
By Deduction By Inductiou 

or Synthesis or Analysis 

in Teaching in Learning 

or Verification or Invention 

or yevsaig [Ar.) or EvpEaig (Ar.) 

we proceed 
From Law To Fact 

Eule Example 

Cause Effect 

dioTi {Ar.) Srt (Ar.) 

airb Tuv upxuv {A.r.) i^i rd.g upxac. (Ar.) 



278 OUTLINE OF Till'; 

astronomer, the geologist conducts his operations with 
composure and success, Avere once bare possibilities, 
which after being handed back and forward between 
Induction and Deduction, turned out to be truths. 
This leads on to other considerations, first as to the 
Modality of Judgments, that is, the degree of our 
belief in them, and next as to the use of the Syllo- 
gism in the procedure just described. 

§ 118. Beliefs and Decrees of Belief. 

In forming any judgment we cannot avoid attach- 
ing to it a particular degree of credence, which might 
be, and often is, expressed by the insertion of some 
adverb to qualify the copula ; thus " To-morrow \\dll 
(possibly) be fine," and " Two straight lines (indis- 
putably) cannot enclose a space." Although one of 
these judgments admits a degree of doubt, which the 
other excludes, the difference lies in our knowledge 
of the things spoken of, rather than in the things 
themselves. To-morrow will be fine or will be 
stormy, and it is fixed by the laws of nature which 
shall happen ; but to us the matter is purely doubtful, 
because we cannot see into the order of nature as to 
this particular. Doubtful statements may become 
certain, without any alteration in the facts to which 
they relate, by changes in our knowledge. A child 
sees with wonder a lunar eclipse, and thinks that 
possibly another may happen to-morrow ; when he has 
learnt Astronomy he may be able to say from exact 
calculations upon what day one may positively be 
expected. Yet here the order of things remains the 
same. The amount of belief which we have in our 



LAWS OF THOUGHT. 279 

judgment has been called its Modality, as being the 
mode in which we hold it for truth. Arranging the 
degrees of Modality in an ascending scale, we find 
that a judgment may be 
^ 1. Possible, where upon the first view we have no 
cause to think that the predicate may not be truly 
said of the subject, but have not examined. Does 
this amount to a judgment or is it the step which 
must precede the formation of the weakest kind of 
judgment ? 

2. Doubtful, where we have tested it in some cases, 
and found that some seem to confirm it, whilst some 
are doubtful. 

3. Probable, where all the trials we have made are 
favourable, but the number of them is not sufficient 
to warrant certainty. 

4. Morally certain for the thinker himself; where 
from examination of the matter, or prejudice, or in- 
terest, he has formed his own belief, but cannot put 
forward sufficient grounds for it, so as to control thai 
of others. 

5. Morally certain for a class or school ; where 
the judgment rests upon grounds which are sufficient 
for all men of the same habits of thought, or the 
same education, as the thinker. 

6. Morally certain for all ; as for example the be- 
lief that there is a future state, which though not ab- 
solutely demonstrable, rests upon such grounds that it 
ought to influence the conduct [mores] of every man. 

7. Physically certain, with a limit ; where the 
judgment is grounded on an induction supposed to 
be complete, but with the possibility that future in* 
duction may supersede it. 



280 OUTLINE OF THE 

8. Physically certain without limitation ; as our 
belief in the law of gravitation, the law of chemical 
affinity, &c. 

9. Mathematically certain ; where doubt cannot 
be admitted. Ex. gr. the axiom — Two straight lines 
cannot enclose a space ; or the theorem — The angles 
at the base of an isosceles triangle are equal. 

"^ All these degrees of belief may, upon a broader 
principle of division, be resolved into three. 

Our judgments, according to Aristotle, are either 
problematical, assertive, or demonstrable ; or in other 
words, the results of Opinion, of Belief, or of Science. 

The problematical judgment is neither subjectively 
nor objectively true, that is, it is neither held with 
entire certainty by the thinking subject, nor can we 
show that it truly represents the object about which 
we judge. It is a mere opinion. It may however 
be the expression of our presentiment of certainty ; 
and what was held as mere opinion before proof, may 
afterwards be proved to demonstration. Great dis- 
coveries are problems at first, and the examination of 
them leads to a conviction of their truth, as it has 
done to the abandonment of many false opinions. 
In other subjects we cannot from the nature of the 
case advance beyond mere opinion. Whenever we 
judge about variable things, as the future actions of 
men, the best course of conduct for ourselves under 
doubtful circumstances, historical facts about which 
there is conflicting testimony, we can but form a 
problematical judgment, and must admit the possi- 
bility of error at the moment of making our decis- 
ion. 
' The assertive judgment is one of which we are 



y 



LAWS OF THOUGHT. 281' 

fully persuaded ourselves, but cannot give grounds 
for our belief, that shall compel men in general to 
coincide with us. It is therefore subjectively, but not 
objectively certain. It commends itself to our moral 
nature, and in so far as other men are of the same 
disposition, they will accept it likewise. 

The demonstrative judgment is both subjectively 
and objectively true. It may either be certain in 
itself, as a mathematical axiom is, or capable of proof 
by means of other judgments, as the theorems of 
mathematics and the laws of physical science. 

§ 119. The Syllogism both deductive and inductive. 

It is a great misfortune for Logic that the Syllo- 
gism has been regarded as an instrument for deduc- 
tion only. An error of Aristotle's, for the correction 
of which his many-sided mind has itself supplied 
hints, has been tenaciously preserved ; and according 
to it, four modes of syllogism, in which we start from 
a general law as our main premiss, have been re- 
garded as the only perfect forms, and opinions have 
been pronounced upon the whole syllogistic system 
from these four specimens. We need not wonder 
then that modes only adapted for teaching truth, 
have been pronounced useless for discovering it ; that 
when deductive arguments are selected, it should be 
easy to prove that they wiU not do the work of in- 
ductive. But it is wonderful that so few should 
have perceived how absurd were the attempts to turn 
the so-called imperfect modes into perfect ones. It 
has been shown already (p. 210), that the modes of 
oach figure in the old arrangement had their propei 



282 OUTLINE OF THE 

use, that the first served for deducing facts from laws, 
the second for establishing differences, and the third 
for bringing in examples and exceptions. Yet logi- 
cians have persisted in tortm*ing syllogisms of the 
second and third figures into the first, by the help of 
Conversion, vv^ithout perceiving that they turned a 
natural argument into a distorted monster. To say — 

^ (A A I, Fig. III.) 

Lead is fusible. 

Lead is a metal ; 

Therefore some metal i& fusible — 

is natural enough ; bat it partakes far more of the 
nature of induction than deduction, because it is 
advancing from a single observation towards a more 
general statement, which may end probably in a 
• universal. Now to establish the erroneous assertion 
that all syllogisms are deductions, logicians are 
bound either to deny that such an argument is a 
syllogism, or to attempt to reduce it to one of the 
deductive modes. They adopt the latter alternative, 
thus — 

(All, Fig. I.) 

Lead is fusible, 

Some metal is lead ; 

Therefore some metal is fusible. 

But this unnatural form is no more like deduction 
than before ; there is no reasoning from a law to 
facts, from a general to a particular statement, and 
all that has been done is to give us for a second 
premiss an unnatural judgment such as logicians 
have taught us already to avoid as much as possible, 



LAWS OF THOUGHT. 283 

The syllogism is not confined to deductive argu- 
ments. Every one of the inductive methods already 
described, falls easily into an appropriate syllogistic 
form ; and we can no more reason without making 
syllogisms than we can speak and argue without 
forming sentences. What Grammar does for speech 
Logic does for thought ; it ascertains its simple 
elements and exhibits them, and if it be found that 
the inductive processes do not fall readily under the 
old forms, it would be right to consider first whether 
the forms could be amended or enlarged, rather than 
to abandon at once one half the territory of thought, 
the whole of which Logic has always by its names 
and definitions seemed to claim. 

To assign one half the domain of Logic to Induc- 
tion is not strictly correct. There is in truth a third 
process, of some subordinate advantage in investiga- 
tion, whereby no advance is made towards general 
laws, as in Induction, nor towards the application 
of laws to facts, as in Deduction, but the matter of 
knowledge is exhibited under a new and more 
convenient form. It has been appropriately named 
Traduction.* The modes U U U in all the figures 
are those which exemplify it most perfectly. 

§ 120. Employment of defective Syllogisms. 

The difficulty in answering the question— how 
does Logic aid by the syllogism in adding to our 
stock of knowledge ? has been caused principally by 
studying only the complete forms of syllogism, 

* By Mr. James Broun, in an able letter in Prof. De Morgan'$ 
Formal Logic, p. 332 



284 OUTLINE OF THE 

whereas in discovery it is necessary to accept de« 
fective forms, only suspending our adoption of them 
until they are fortified by other evidence. The fact 
that such suspense is necessary proves that the 
forms are imperfect; the fact that we have attained 
new truths from evidence formally insufficient to 
establish them by itself, proves their usefulness. 
This will appear from a description of some of the 
best known forms of defective syllogism. 

The E-HETORiCAL Enthymeme as described by 
Aristotle, is " a syllogism from probable propositions 
or from signs." The probable proposition (eZ/cof) is 
that sort of statement which must satisfy us in mat- 
ters where universal assertions are impossible ; as in 
human alFau-s, that " injured men will seek revenge 
— men are active where their interest is concerned," 
and the like. Any syllogism into which a propo- 
sition of this sort, general but by no means universal, 
enters, can only supply a general and therefore un- 
certain conclusion. The sign (aijfLeiov) according to 
Aristotle, is a proposition in which some one fact or 
mark that accompanies, precedes, or follows, another 
fact or conception, is adduced as a necessary or 
probable indication that the other is present. (Pri. 
An. ii. 27.) In describing a sign as " a proposition," 
some violence is done to language, since it can 
always be expressed as a single term. As no ac- 
count is taken of negative signs, indications, that is, 
that a given thing does not exist, all the Enthy- 
memes based on signs will be positive or affirma- 
tive; and as they are to prove the existence of a 
given fact without limitation, their conclusions will 
also be universal. Now some of them are found to 



LAWS OF THOUGHT. 285 

furnish demonstrative proof of the point they would 
establish ; and these are called Proofs. Others only 
afford a presumption more or less valid that the 
conclusion is true. This difference becomes mani- 
fest from the use of the three Figures ; the Proofs 
will only be found, where the mode and figure of 
the syllogism, made out of the terms of the question 
with the sign for a middle term, are logically valid. 
Where they are invalid, the sign will fall short of a 
Proof to the extent of that invalidity. Thus, of 
three Enthymemes ; (i.) Dionysius must fear be- 
cause he is a tyrant ; (ii.) This man is the murderer, 
because he was near the murdered man ; (iii.) As 
we see from the case of Lord Bacon, contemplative 
men are competent to the affairs of life ; — each falls 
into a different figure. 



(i. A A A.) 

All tyrants fear, 
Dionysius is a tyrant ; 
• He must fear. 



(ii. A A A.) 



The murderer -would be near. 
This man is near ; 
' He is the murderer. 



(ill. A A A.) 

Lord Bacon was a practical man, 
Lord Bacon was contemplative ; 
".• All contemplative men are fit for practical life. 

Of these the first alone is formally conclusive, be- 
cause it violates no syllogistic rule ; it amounts there- 
fore to a scientific proof. Not so the second ; it has 
not distributed the middle term ; it should have 
shown not only that the murderer must be near, but 
that he alone could be so. The third again draws 
a conclusion far too wide for its premisses ; what ia 



280 OUTLINE OF THE 

true of Lord Bacon need not be so of the whole clags 
from which he has been selected. On reference to 
the table (p. 210) it will be found that A A A is 
omitted both from the second and third Figures, in 
consequence of these defects. But are these imper- 
fect modes quite useless ? Far from it. A single 
argument of this kind establishes a presumption of 
agreement between the terms of the conclusion, and 
instigates to the search for other confirmatory signs. 
But several concurrent Enthymemes are often a8 
cogent as a demonstrative syllogism. In the inves- 
tigation of the authorship of the letters of Junius, 
Mr. Taylor employs of necessity a string of enthy- 
memes in the second Figure, each in itself defective, 
but altogether forming a very strong case. Thus, 

The author of " Junius " wrote a particular hand, 
Sir Philip I'rancis -wrote the same kind of hand ; 
Therefore Sir Philip Prancis is the author of "Junius." 

The author of "Junius" made certain mistakes in correcting 

proof-sheets, 
Sir Philip Prancis made the same mistakes ; 
Therefore Sir Philip Francis is the author of " Junius." 

The author of " Junius " had a particular style, 

Sir PhiUp Prancis wrote the same style ; 

Therefore Sir Philip Prancis is the author of " Junius." 

The author of " Junius " is guilty of an anomalous use of certain 

words. 
Sir Philip Francis is guilty of the same ; 
Therefore Sir Philip Francis is the author of " Junius.'' 

The author of "Junius " employs certain images, 

Sir Philip Francis employs the same ; 

Therefore Sir Philip Francis is the author of " eTunius." 



LAWS OF THOUGHT. 287 

The author of " Junius " ceased- to write at a particular time, . 
Sir Phihp Francis must have ceased to write at the same time ; 
Therefore Sir Pliihp Francis is the author of "Junius." 

The results of these and several similar arguments 
are summed up in a syllogism which most people, 
unless they could assail the truth of some of the 
statements, would think conclusive, to the effect that 
two persons who in so many points are not found to 
differ must be one and the same. Circumstantial 
evidence falls naturally into a series of Enthymemes 
of the second figure. Those of the third figure are 
employed in inductive reasoning ; and a series of 
them might afford a very high degree of probability 
that the conclusion common to all was true. Aris- 
totle's doctrine of Enthymemes differs from the or- 
dinary view of syllogism, only as to the order of 
statement of these as distinguished from common 
syllogisms, and the license allowed to employ pro- 
visionally, defective arguments, where better cannot 
be found. In any syllogism whatever, if we regard 
the question or conclusion first, as Aristotle does in 
this case, we may call the middle term a sign of its 
truth : but it is an important admission that signs 
may be used which do not prove the question, and 
only establish a presumption stronger or weaker in 
its favour. 

The Example is an argument which proves some- 
thing to be true in a particular case from another 
particular case. Thus " Harvey might expect to be 
persecuted for his discovery of the circulation of the 
blood, because Galileo was for his discovery." But 
the cormection between two distinct facts can only 
depend upon their coming under some common law 



288 OUTLINE OF THE 

and therefore in the Example the proof is not of one 
particular judgment by another, but of a particular 
by means of a universal, for which another particular 
is the sign. Thus 

(Enthymeme in A A A, Fig. in. with Episyllogism in A A A, 
Fig. I.) 

Galileo was persecuted, 

Galileo was a discoverer in science ; 

Therefore all discoverers are likely to be persecuted. 

Harvey is a discoverer. 

Therefore he too will be persecuted. 

This argument is called " rhetorical induction ; " it 
differs from induction* proper in bringing in only 
one example instead of many, and in going on to 
prove another particular case, instead of stopping 
at the general law. The flaw in it is obvious ; but 
the nearer the predicate of the second premiss ap- 
proaches to distribution, the less probable is an error. 
If it could be shown that " Galileo was a fair sample 
of all discoverers," the mode would become A U A, 
Fig. III. which is formally correct. But in its weaker 
form it is perpetually employed. 

The Induction by Imperfect Enumeration is an 
argument which establishes a general law or rule 
from a number of examples of it less than the whole. 
Thus 

(In A A A, Fig. iii.) 

Gold, silver, and copper melt. 

They are metals ; 

Therefore all metals will melt. 

* This difference disappears if with Diogenes Laertius, and Cicero, 
we describe Induction as an argument from particulars to like partic- 
ulars. Heydcr, Dartstellung, p. 60. 



LAWS OF THOUGHT. 289 

Its formal fault is the same as that of the Enthy- 
meme of the 3d Figare (p. 285), with which it is 
almost identical ; the conditions on which it may be 
employed have been explained above. 

§ 121. Syllogism of Analogy. 

Analogy has been defined " The similarity of ratios 
or relations ; " and as each relation supposes two cog- 
nate things, a comparison of relations would imply 
four things and four terms to express them. Thus 
(to employ one of Archbishop Whateley's examples) 
when MandeviUe uses as an argument against popu- 
lar education, that, " If the horse knew enough he 
would soon throw his rider," he intends to imply two 
pairs of related terms — 

As the horse is to its rider, so is the people to its rulers — 

and to assert further that since the one relation de- 
pends upon the continuance of ignorance on the part 
of the horse, the other depends upon ignorance also. 
Common sense suggests the refutation of such an 
argument ; we deny that the relations are similar, or 
at least that the similarity reaches so far as to war- 
rant such an assertion as is founded upon it. Simi- 
larity of relations may exist, however, where there is 
no resemblance between the related things. 

But in popular language we extend the word anal- 
ogy to include resemblances of things, as well as of 
relations. Analogy in this sense has exercised an 
immense influence on the formation of language. 
In innumerable cases visible or tangible things lend 
their names to invisible and spiritual, from a resem? 

19 



290 OUTLINE OF THE 

blance more or less striking between them. Trans- 
gression in its primary sense means the crossing over 
a visible boundary ; right means straight, and lorong 
means twisted. We speak of a clear statement, a 
lofty mind, and a deep thought, all these adjectives 
being drawn from the analogies of the material world. 
"Whilst we can exhibit them in the form of a state- 
ment of proportions, so as to vindicate the original 
sense of analogy, it is not necessary, nor in all cases 
natural, to do so. We may consider therefore that 
similarity of attributes, as well as of relations, may 
have the name of analogy. 

Employed as an argument, analogy depends upon 
the canon — The same attributes may be assigned to 
distinct but similar things, provided they can be shoion 
to accompany the points of resemblance in the things, 
and not the points of difference. But since the pre- 
supposition of a power of discerning to what part 
of the things the attributes belong, is indispensable, 
the argument itself depends for its weight upon 
something external to itself, and sinks into a mere 
exposition. In a syllogism proving that the metrop- 
olis, as the heart of a state, should not be suffered 
to become too large, because a large heart is diseased, 
the real dispute would not be about the syllogism 
itself — 

The heart in relation to the body should not be too large, 
The heart in relation to the body = (partly) the metropolis in re- 
lation to the state ; 
Therefore the metropolis to the state should not be too large. 

This inference (in E U E, Fig. iii.) is faultless, 
provided we admit that the partial identity estab- 
lished between the heart and the metropolis includes 



LAWS OF THOUGHT. 291 

the point of size ; ai>'i to decide this, other arguments 
will be requisite, which, if unsuccessful, will render 
the present one false ; if successful, needless. And 
therefore arguments of this kind, founded on a ques- 
tionable resemblance, are used rather to suggest com- 
parisons, and so persuade, than to compel conviction ; 
and philosophers have had great cause to complain 
of the many fallacies which become current through 
false " metaphorical analogies." 

But where the resemblance between two things is 
undoubted, and does not depend on one or two ex- 
ternal features, analogy tends much more strongly 
to persuasion at least, though it cannot amount to 
demonstration. Its principle would be — When one 
thing" resembles another in knoivn particulars, it ivill 
resemble it also in the unknown. The expression of 
their agreement must be a qualified judgment of 
identity — a U. They must not be of the same kind, 
but only of a similar one, otherwise the argument is 
a mere case of Example. Neither must the usual 
tests have been applied (see p. 258,) to prove that 
the known particulars invariably accompany the un- 
known, otherwise, as Mr. Mill observes, we trench 
upon the ground of Induction. In venturing thus to 
assign attributes to a thing, because other things of 
a different class have them, we show our dependence 
on the regularity and consistency of creation. When 
the geologist discovers a fossil animal with large 
strong blunt claws, he infers that it procured its food 
by scratching or burrowing in the earth, trusting 
that a conformation which in other kinds of animals 
accompanies this particular mode of life, would not 
be arbitrarily and exceptionally assigned in this case 



292 OUTLINE OF THE 

to an animal of different pursuits. The following 
example, from Bishop Butler, of a false analogy, and 
its refutation, will show the syllogistic treatment of 
analogies : — 

" There is little presumption that death is the destruction of human 
creatures. However, there is the shadow of an analogy, which may 
lead us to imagine it is — the supposed likeness which is observed be- 
tween the decay of vegetables and of living creatures. And this 
likeness is indeed sufl5cient to afford the poets very apt allusions to 
the flowers of the field, in their pictures of the frailty of our present 
life. But, in reason, the analogy is so far from holding, that there 
appears no ground even for the comparison, as to the present ques- 
tion ; because one of the two subjects compared is wholly void of 
that which is the principal and chief thing in the other, the power 
of perception and of action ; and which is the only tning we are in- 
quiring about the continuance of. So that the destruction of a veg- 
etable is an event not similar, or analogous, to the destruction of a 
living agent." 

This may be resolved into two syllogisms. 

I. Analogy — ^in A U A, Fig. in. 

The decay of vegetables is total destruction, 

The decay of vegetables=(for present purposes) the decay of liv- 
ing creatures ; 
Therefore the decay of living creatures is total destruction. 

II. Refutation — in A E E, Fig. ii. 

The decay of animals is that of living, acting creatures, 
The decay of vegetables is not that of living, acting creatures ; 
Therefore the decay of vegetables is not the same as that of ani- 
mals. 

The conclusion E of the latter syllogism is opposed 
*is a contrary to the premiss U of the former. 



LAWS OF THOUGHT. 293 

§ 122. Syllogisms of Chance. 

Chance* may be described as the amount of 
belief with which we expect one or other, out of 
two or more uncertain events. Uncertain events are 
those wherein no cause or law appears, to determine 
the occurrence of one rather than of another. As 
all questions into which this notion enters demand 
a numerical statement, the doctrine of Chances is 
usually regarded as a branch of mathematics; and 
its intricacies can only be explained by persons 
deeply conversant with that science, who have 
turned their attention to this special- branch of 
inquiry. Only the bare elements of it can be given 
here, with a few of the simplest examples. 

1. The first principle is that the probability of an 
uncertain event is represented by the 7iumber of 
chances favourable to an event divided by the total 
number of chances. Thus the chances that a pic- 
tured card will be drawn out of a pack at random, 
the first attempt, are \% because there are fifty-two 
cards that may be drawn, and only twelve pictured 

* The materials of this section are taken entirely from Quetelet on 
Probabilities (of which most interesting work there is a readable 
and spirited translation by Mr. G. 0. Dowries), and from the Formal 
Logic of Professor De Morgan, 'whose researches, there, in the Cam- 
bridge Philos. Trans., and in the Encyclopsedia Metrop., are spoken 
of by those better able to follow them than myself, as very acute 
and profound. Professor Donkin (Philos. Mag. May, 1851) has 
developed with great clearness the view, common to him and to the 
writers I have named, that " the subject-matter of calculations in 
the theory of probabilities is quantity of belief. In every problem a 
certain number of hypotheses are presented to the mind, along with 
a certain quantity of information relating to them : the question is — 
in what way ought belief to be distributed among them ? " Hij 
researches did not come under my notice till the text was written. 



294 OUTLINE OF THE 

cards to furnish the desired result. If it is v/ished to 
balance the chances on each side, the twelve favoura- 
ble must be subtracted from the whole fifty-two, and 
forty unfavourable are found to remain. Applying 
this principle, we should see without much, con- 
sideration that a proposition absolutely certain must 
be represented by a unit, because there is no differ- 
ence between the number of favourable events and 
the whole events. That the card drawn will be of 
some suit or other is certain ; then its chance is 
§5=:1. It is equally clear that the symbol of a 
wholly uncertain judgment is |, for the two chances 
are that it may come to pass or not, and the former 
of them is the one favourable chance. Thus that a 
red card will be drawn, and not a black, will be 

26 1 

52 ii* 

To take a familiar, yet somewhat more difficult 
problem — what are the chances, in tossing up a half- 
penny, that it will give a head at or before the third 
throw? We assume that the sides of the coin 
evenly balance each other, which by the way is not 
the case. Now here are eight events, any one of 
which may occur in three throws — 

1. No head may be thrown. 

2. The 1st throw only may be a head. 

3. The 2d 

4. The 3d 

5. The 1st and 2d 

6. The 1st and 3d 

7. The 2d and 3d 



8. All three may be heads. 
Out of the eight, the first alone is adverse ; in all 



LAWS OF THOUGHT. 295 

the rest a head is thrown at or before the third trial ; 
and according to the axiom, the favourable chances 
are seven (events) to one (event) ; or ^ of the cases 
make for us. 

That this result is fairly calculated may be gath 
ered from another mode of proof. Suppose that 
eight distinct trials are made, to see at what throw 
the first head comes; we may calculate that in seven 
out of the eight trials it is likely to occur at ot 
before the third. As heads are as likely to be 
thrown as tails, we expect that in half, that is, four 
cases, heads will make their appearance the first 
time. The same principle applies to the other four 
cases, in which we must go on to a second tlirow ; 
in half of the second throws, that is, two, we expect 
heads. There remain only two cases in which it 
will be necessary to proceed to a third trial, to get 
the head ; and half of them, or one, will be heads. 
Thus— 

In 4 cases, a head first throw. 

In 2 , second . 

In 1 , third . 



leaving only one of the eight trials in which it will 
be necessary to go further. Here again we have 
seven favourable events to one unfavourable ; in 
common language the odds are seven to one. 

There is no difficulty in stating the result thus 
attained, in a syllogism. 

I of the groups of three throws give a head. 
This trial is to be a group of three throws ; 
Therefore this trial (I) will give a head. 



296 outlinp: of the 

The fraction written after the subject of the eon- 
elusion is to be read " It is 7 chances out of 8 ; " 
or, taking the numerator for the chances on the 
one side, and the difference between it and the 
denominator for those on the other, " The chances 
are 7 to 1." 

The origin of the axiom is involved in the same 
difficulty as attends the axioms of geometry. How 
do we come to expect that in the long run head and 
tail will nearly divide the throws between them ? 
Why do we not look for a long unbroken series of 
one or the other? Experience, no doubt, first sug- 
gested this absolute indifference of nature to two 
events, neither of them having any known cause 
that should give it a preponderance. But it may 
still be questioned whether the intricate calculations 
founded on this axiom are mere generalizations of 
experience, and w^hether our faith in the necessary 
truth of the axiom be not more than the sum of our 
experiments. Certain it is that experience confirms 
it. In experiments made by BufFon, by Professor de 
Morgan, and M. Quetelet, the results coincided very 
closely with the a priori calculation. But to verify 
the doctrine of chances by experiment, a wide range 
of facts is required, because a series of a few cases 
often exhibits great aberrations from a rule that 
never fails to vindicate itself in a lonafer course on 
trials. An Insurance Office, with five or ten clients 
only, might be ruined in a year by two deaths. In 
some of the experiments alluded to above, a head 
was not thrown till the 10th, the 14th, and the 16th 
throws. It is not unusual to find a family with six 
or eight sons and no daughters ; and yet the whole 



LAWS OF THOUGHT 297 

number of male is very nearly equal to that of fe- 
male births throughout the ^vorld, 

2. Where the probability is a compound one, that 
is, where one uncertain event depends upon another, 
the rule is that the whole probability is ascertained 
by multiplying the chances of the separate events to- 
gether. Imagine a gold, a silver, and a leaden urn, 
the first containing four white and two black balls, 
the second and third six white balls each ; and sup- 
pose that a man is to draw one ball blindfold from 
one of the three urns, he knows not which, — what 
are the chances of his fixing on a black ball ? The 
black ball can only be drawn from the golden urn ; 
and the chance that he goes there at all is § : if he 
finds that urn, the black balls in it are | of the whole; 
then the chances of his drawing a black ball are 
i X 6 ^= il == §. By way of proof that the sum total 
of the chances is not altered by their having been 
distributed over two events, it is to be noticed that 
if all the 18 balls were in one urn, the chances would 
be exactly the same. The syllogism would be — 

My drawing from the golden urn is I of the possi- 
ble cases. 

My di-awing a black ball is | of the possible draw- 
ings from that urn ; 

Therefore my drawing a black ball is \ of the 
possible cases. Or — 

B is I A, 

C is I B ; 
. • . C is I A. 

In other words, there are 15 to 2, or 8 to 1, against 
my drawing a black ball. 



298 OUTLINE OF THE 

3. To find the chance of the recurrence of an 
event akeady observed, divide the number of iimf 
the event has been observed, increased by one, by ilH 
same number increased by tivo. If an inlander coming 
to the sea, observed the phenomenon of the tide 
ten times in succession, the chance to him that at 
the next period the tide would again rise would be 
^^-^rrr- ) or 11 to 1. Every certainty is represented 

by a unit, as has been shown ; and so many units 
are added to the possible cases (denominator of the 
fraction) as there have been events, and so many to 
the favourable cases (numerator) as there have been 
favourable events. " Or, if we represent," says M. 
Quetelet, " the number of times that the event has 
occurred by a similar number of white balls that 
we throw into an urn, adding also one othei white 
ball and one black ball, the probability of the rv'ipro- 
duction will be equal to that of drawing a white ball." 
4r In order to calculate the probability that an 
event already observed will be repeated any given 
number of times, the rule is, to divide the number of 
times the event has been observed, increased by one, 
by the same number increased by one and the number 
of times the event is to recur. Thus, if the tide had 
been observed 9 times, the chance that it v/ould recur 
ten times more would be -g ^ ,oI|;t=( *2o')= !• " "^^^^ 
is the same thing as if each reproduction of the ob- 
served event corresponded to putting a white ball in 
an urn where there were already, before commenc- 
ing the trials, a white ball and as many black balls as 
it is supposed that the event observed should re-occu/ 
times." 



LAWS OF THOUGHT. 299 

5. The probability that there exists a cause of the 
reproduction of any event observed several times in 
succession is expressed hy a fraction ivhich has for its 
denominator the number 2 multiplied by itself as many 
times as the event has been observed, and for its nu- 
merator the same product minus one. This has been 
called Bayes's rule, and its validity is not so generally 
admitted as that of the preceding ones. Thus, sup- 
posing the two tides only had been observed, the 
chance of a cause would be 

2X2X2-1 7 



2X^X2 ** 

Where the observations have not all been favour- 
able, in order to estimate whether the event will 
occur once more, the rule is to divide the number of 
times the event has been observed to happen increased 
by one, by the total number of observations increased 
by two. Thus, if out of 26 metals known to the 
chemist, 24 are heavier than water and 2 lighter, the 
chance that the next discovered, assuming as certain 
the fact of discovery, will be lighter than water will 
be Ul=^ ; °r 25 to 3. 

Other examples of these formulae may readily be" 
found, to make the use of them easy, and to verify 
their truth. In applying the doctrine of chances to 
that subject in connection with which it was invented, 
— games of chance — the principles of what has been 
happily termed " moral arithmetic " must not be for- 
gotten. Not only would it be difficult for a gamester 
to find an antagonist on terms, as to fortune and 
needs, precisely equal, but also it is impossible that 
with such an equality the advantage of a consider- 



300 OUTLINE OF THE 

able gain should balance the harm of a serious lo^is. 
" If two men," says Buffon, " were to determine to 
play for their whole property, what -would be the 
effect of this agreement? The one would only 
double his fortune, and the other reduce his to 
naught. What proportion is there between the loss 
and the gain ? The same that there is between all 
and nothing. The gain of the one is but a moderate 
sum, — the loss of the other is numerically infinite, 
and morally so great that the labour of his whole life 
may not perhaps suffice to restore his property." 

The theory of chances assists materially in giving 
a clear conception of modality (p. 278). A propo- 
sition may pass from absolute uncertainty where 
there is as much against as for its truth (=: I) up to 
absolute certainty (= 1) through an infinite number 
of deepening shades of probability (f, |, ^^%, and so 
on). These refinements in estimating evidence are 
little used in ordinary thinking, it is true ; and 
broader lines of distinction suffice. But they seem 
to justify those who exclude modality from the form 
of judgments, since otherwise one judgment would 
seem to be capable of being modified into a hundred, 
the expression remaining the same, and the evidence 
only varying. 

Hume in his " Essay of Miracles " has overlooked 
one property of highly probable judgments — that the 
favourable evidence for them not only preponderates 
over, but utterly expels, the unfavourable, and es- 
pecially in matters where the moral nature is con- 
cerned. The probable evidence that the sun will rise 
daily for the next ten years is exceedingly strong : 
and consequently, frorn " the days of Noah " to the 



LAWS OF THOUGHT. 301 

present, people have acted as if the weaker proba- 
bility had no existence. If a jury find a man guilty, 
because ten credible witnesses have sworn against 
him, and one or two for him, they consider that the 
testimony of the ten annihilates that of the two ; 
were it otherwise, they must give the prisoner the 
benefit of their doubt. A son does not estimate the 
balance in favour of the truth of a father's statement, 
nor a friend of a friend's : because to doubt at all is 
not to believe. When he asserts that in the case of 
miracles, " there is a mutual destruction of arguments 
[for and against them], and the superior only gives us 
an assurance suitable to that degree of force which 
remains after deducting the inferior," he neglects the 
distinction between mathematical and moral subjects ; 
in the one, both favourable and adverse chances must 
be preserved ; in the other, that is, where we have to 
act on probabilities, adverse arguments must, when 
once we have made up our minds, be ignored entirely, 
because to permit them the smallest influence would 
weaken and fetter our actions. The rest of his ar- 
gument has been fully refuted. Writers on proba- 
bilities have shown how rapidly the scale of belief 
ascends with the addition of each new independent 
witness ; and Paley has exposed the fallacy of rea- 
soning from what is contrary to one's own experience 
to what contradicts the universal experience of men. 
The numerical mode of statement illustrates the 
operation of the will in moral actions. The action 
entirely indeterminate, in which there is an exact 
equilibrium between the motives for and those against 
a particular course, is represented by (say) i^'g = § ; 
though some maintain that except in the case of the 



302 OUTLINE OF THE 

ass of Buridanus, whose '• two bundles of hay " are 
no longer worthy of the dignity of philosophy, so 
nice a balance cannot occur. The necessary action, 
where all the motives are on one side, is represented 
by IqI = 1. Between these extremes a vast number 
of degrees must exist; and though human justice 
draws a broad line where criminal responsibility be- 
gins, its decisions must needs be rough and inaccu- 
rate. 

The application of the doctrine of chances to real 
cases must be made with great caution. Our illus- 
trations have been drawn for the most part from 
artificial cases, where causes have been studiously 
excluded that might have disturbed and complicated 
the results : in nature these are hard to find. 



§ 123. Syllogisms of Classification. 

Classification, which enters into all sciences, is the 
basis of some of them, as Botany, Mineralogy, and 
Zoology. In every act of classification two steps 
must be taken ; certain marks are to be selected, the 
possession of which is to be the title to admission 
into the class, and then all the objects that possess 
them are to be ascertained. Where the marks se- 
lected are really important, and connected closely 
with the nature and functions of the thing, the classi- 
fication is said to be natural ; where they, are such 
as do not afiect the nature of the objects materially, 
and belong in common to things the most different 
in their main properties, it is artificial. 

A class cannot always be defined in words, so as 
to describe every species in it. From the lowest of 



LAWS OF THOUrTHT. 303 

ts subdivisions to the highest, we pass through so 
many shades of difference, that we had a difficulty 
in perceiving and expressing the lilieness between 
the extremes ; and properties which were prorainen-f 
at the bottom of the scale, are in the higher steps 
forgotten, as nobler ones come into view. To dis- 
tinguish the polyp, the lowest species in the animal 
series, from a plant, it must be defined as "having 
a digestive cavity ; " whereas the definition usually 
given for higher animals, and for the conception 
animal in general, conveys that they are "beings 
endowed with life and sensation." Still we group 
them together by our perception of likeness ; which 
though not so obviously applicable to the ends of 
the series viewed together, and apart from the inter- 
mediate links, become so when we pass regularly 
along the chain. We might not be able to prove 
that the polyp had sensation at all, if there were not 
creatures a little higher in the scale of being, re- 
sembling the polyp in other particulars, and exhibit- 
ing more plainly the sense of feeling. We presume 
that it exists in the lower, because we see it in the 
higher, and though it decreases as we descend, we 
cannot show that it has ceased. The definition of a 
genus is the adequate definition of its lowest species 
only, since one which included any higher properties 
than the lowest exhibits, would of course exclude it. 
But in classification, the definition is not so much 
used as the type, by likeness or unlikeness to whli^h 
we arrange the others, and assign them a higher . i 
lower degree. 

Though the species in any great class rise by the 
steps of a regular arrangem«^.nt, the same series must 



304 OUTLINE OF THE 

not be continued from the highest of one kingdom to 
the lowest of the next above it. The highest plant 
is often considered next below the lowest animal, 
Vhereas it is much more like, though infinitely in- 
ferior to, the highest animal. The animal, vegetable, 
and mineral kingdoms rather resemble ladders of 
equal height resting upon three different steps of a 
house, than ladders raised one upon the other. The 
lowest animal, the lowest plant, and the lowest min- 
eral answer to each other ; and the complex animal 
organism, the tali and beautiful tree, and the regular 
group of crystals correspond in some measure at the 
top of the respective scales. 

A syllogism like the following is adapted to ex- 
press classification. 

(UAA. Fig. I.) 

All beings endowed with life and sensation = animals, 
The polyp .... the man have life and sensation ; 
Therefore they are animals. 



§ 124. Nomenclature. 

The fourth question to be answered was — How 
shall new laws be expressed and recorded ? It has 
been shown already (p. 44) that names are useful in 
preserving the results of new discoveries and reason- 
ings, and that without such means science could 
never secure its gains, nor reproduce them with the 
necessary celerity. Let any one consider how much 
is meant by chemical affinity, atomic weight, capital^ 
inverse proportion, polarity, means, and litnits ; how 
theories are here gathered up into a single word, and 



LAWS OF THOUGHT. 305 

passed readily from mind to mind; and he will 
admit the parallel between words and that paper 
money by which the ponderous wealth of the world 
may be enclosed in envelops, and passed swiftly 
from hence to the antipodes. Hence every progres- 
sive science must constantly enlarge its store of 
names and words. Four ways are open to it of 
doing so.* 

1. Names already in use may be adapted to new 
meanings, by fresh definitions. Thus salt has been 
extended, from the condiment still known by that 
name, to a great class of compound bodies known to 
the chemist. Force, attraction, affinity afford other 
examples. 

2. Names that contain their own explanation may 
be formed, to represent new ideas ; as isomorphism 
for the identity of the crystalline forms of some 
chemical bodies ; TrpoaipeaLg, to express the previous 
choice or purpose which makes our actions morally 
imputable to us ; homoeopathy for the system of med- 
icine that professes to cure by medicines that produce 
effects like the disease. Names so constructed will 
often embody a theory, and should be discarded if it 
turns out to be untrue. 

3. The invention of a wholly new name, unmean- 
ing in itself, but accompanied by a precise definition, 
is free from some of the dangers that beset the other 
modes ; for old words are often used vaguely, because 
they have obtained a footing before their scientific 
meaning has been given them, and new names that 
convey their own explanation are often cumbrous, 

* For fuller illustrations, see Whewell's Philosophy of the Indue 
tive Sciences. 

20 



306 OUTLINE OF THE 

and in souie caises do not permit the erroneous the- 
ory they carry on their face, to be amended. An 
attempt of this kind has been made by Von Keich- 
enbach, in designating a new force he believes that 
he has discovered by the name Ot^-force. Such a 
name, whatever be thought of the theory it belongs 
to, seems well devised ; it is short and easy of use, 
and it enters readily into compounds, as Odyle, 
Thermodyle, and so on. 

4. Chemistry affords good examples of the mode 
of forming new names by systematic alterations of 
old well known ones. Thus from sulphur we have 
sulphide, sulphite, sulphate, bisulphate, &c. and each 
of these is appropriated to a particular chemical con- 
stitution. Such a plan seems to obviate the objec- 
tions on the score of novelty, vagueness, and transi- 
toriness, to which other methods are open. 

§ 125. Sources of Principles. 

The inductive and deductive processes presuppose 
some principles from which they may commence. A 
principle might be defined as that from which reason- 
ing begins. 

Observation:^ either by means of the senses unaided, 
or by the assistance of instruments, furnishes the 
principles of inductive reasoning. Where isolated 
observations are of less value, from their fluctua- 
tions, as ill estimating the temperature of the coun- 
try, the weight of the atmosphere, and the like, the 
doctrine of means is applied to an extended series of 
observations. By it, the sum of the results of the 
observations is divided by the numbers of observa* 



LAWS OF THOUGHT. 307 

tions taken, and the quotient is the mean. Although 
this may happen not to correspond exactly with a 
single observation, yet in a large number of them it 
is found that the majority range themselves closely 
round the mean, and that the number diminishes 
with surprising regularity as we approach either ex- 
treme. Thus, if the mean temperature on a given 
day in the year be 60^ Fahrenheit, as ascertained 
from the observation of a hundred years, and 50° 
and 70° be the extremes on either side, we shall 
find on arranging the single observations that most 
of them cluster as it were around 60°, whilst one or 
two only coincide with each extreme ; and that as 
the mean is approached, say by intervals of two 
degrees, the number of coincident observations grows 
greater at each step till the mean is reached. A full 
explanation, intelligible \o all, of this most interest- 
ing subject, is given in Quetelet's work " On Prob- 
abilities." Where a mean is taken, without any need 
for arranging the several observations according to 
their approach to it, it has been called an average ; 
the results of the harvest, and the prices of corn, are 
estimated in this way every year, the former roughly, 
the latter with arithmetical accuracy. 

Historical records are observations which rest upon 
the testimony of others ; of these the most important 
are the records of religious history, which rest upon 
outward testimony accepted and confirmed by the 
inward religious consciousness. 

Deductive principles are certain universal proposi- 
tions gained in various ways. Theological principles 
are the truths of the divine law, made known to man 
by inspiration ; universal, but not generalized from 



308 



OUTLINE OF THE 



experience by observation. Natural principles are 
propositions in morals, government, and the like, 
upon which there is a general agi'eement founded 
upon a natural instinct. Mathematical principles 
are propositions about space and number, to which 
the reason cannot but assent, without requking to 
verify them by new trials ; such are the definitions 
and axioms of geometry. Positive principles have 
been gained by reasoning upon former experience ; 
they are either the definitions of the mixed sciences, 
or divisions of their subject matter, or hypotheses 
laid down to be verified by future comparison with 
facts. 



TABLE OF PRINCIPLES. 

N.B. This is not a perfect logical division ; ex.gr. " Observations *■" 
may depend on testimony and so be " histoi-ical." 



' Inductive 



Principles 



Simple 
Observations 



Without instruments 



"With instruments. 



Aggregate f ^"^^^^ ^^ rnQms. and Umit* 
Observations [ Sunple averages. 
Historical Records. 

' Theological 
Mathematical 



[ Deductive 



Natural 
_ Positive 



' Definitions 
Divisions 
Hypotheses. 



LAWS OF THOUGHT. 309 

§ 126. Errors and Fallacies. 
Not one logical principle can be put in practice 
without the possibility of error. "Where an error is 
latent, and tends to deceive either the thinker or 
those to whom he offers it, the name oi fallacy is 
given to it. A complete list of fallacies would in- 
clude one or more for every one of the processes of 
thinking ; and, after all, the exposure of material er- 
rors can only be effected with advantage by each 
separate science for its own department, as has been 
done for Political Economy in the ^^ Sophismes Eco- 
nomiques" of M. Bastiat. Formal errors are only 
deviations from the laws of thought already laid 
down, as, for example, by making an incomplete 
division, or by holding contradictory judgments to- 
gether, or by drawing a conclusion too broad for the 
premisses. 

§ 127. Dealing- with Errors. 

When opposing arguments are to be dealt with, 
we may either assail one of the premisses by an 
Instance (evaracnc) to the contrary of what it asserts ; 
or we may dissolve {avelv) the argument by showing 
its unfitness for proof because of some formal defect, 
as where a universal is proved from a few particu- 
lars. Or, admitting the apparent correctness of the 
opposing argument, we may prove the contradictory 
of its conclusion by an unassailable argument of our 
own, which is then called an Elenchus {I'X.eyxoi). Or 
lastly, we may fortify our own argument by " a 
reduction to impossibility," that is, by showing that 
something impossible or absurd follows from con- 



310 OUTLINE OF THE 

tradicting our conclusion ; this is called indirect de- 
monstration, as it goes round to prove that a thing 
is by showing what absurdity would follow if it was 
not, and thus differs from the direct mode, which 
proves directly from premisses that the thing is* 

B. Arrangement of a Science. 

§ 128. Method. Definition and Division, 

As method in the highest sense is a natural gift 
rather than a technical system, it can be best under- 
stood by studying a few examples, which have pro- 
ceeded from minds of the highest order. It will be 
found that whilst the deductive and the inductive 
orders have been followed, wdth the aid of definition 
and division, none of these means has been exclu- 
sively employed ; and the due admixture of them, 
and the degree of preponderance to be assigned to 
any one, have been regulated by the imagination 
and taste of the constructor. In " Euclid's Ele- 
ments," the nature of the subject, which is inde- 
pendent of verification from facts, permits an almost 
exclusively deductive order to prevail, which proceeds 
from definitions and axioms, and dispenses with di- 
vision. In " Plato's Republic," one of the noblest 
examples of method, successive definitions of justice 
are brought to the test and rejected ; and then di- 
vision preponderates, in the enumeration of the 
powers of the human soul, and of the classes in a 
state that answers to them ; as well as of the declina- 

* Instance, Pri. An. ii. 26; Solution of an Argument, Ehet. i. 2, 
Pri. An. II. 27; Elenchus, Pri. An. ii. 20; Eeduction to Impossi 
bihty, Pri. An. i. 23, Post, An. i 26. 



LAWS OF THOUGHT. 311 

tions through which the perfect polity, if it could 
be constructed, would have to pass. The whole is 
fused together and adorned by a dramatic element, 
in such a manner as to render this dialogue the 
finest work of pagan philosophy. In the " Nico- 
machean Ethics " of Aristotle, definition predomi- 
nates but with considerable aid from division. Thus 
he enumerates the opinions of men about "the good," 
and rejects all but the right one ; defining that, under 
the name of " happiness," he is led on to define the 
parts of his first definition ; and in the case of the 
moral and intellectual virtues he does not consider 
his explanation complete without an enumeration 
(or division) of both classes. In subordinate por- 
tions, good examples of division are also found ; and 
in the concluding chapters of Book VL, and in other 
places, discussions upon nominal definitions, or the 
senses which various Greek nouns bear, are also in- 
troduced. The text-books of chemistry, mineralogy, 
botany, and zoology, will afibrd good examples of 
division, based upon definition ; a class or type is 
defined, and the species enumerated and examined. 

The close relationship between definition and di- 
vision mil be evident to the student who examines 
such examples carefully. In truth, wherever a di- 
vision is made upon some natural, and not merely 
accidental ground, every step of it furnishes some 
distinctive mark, which will naturally make its ap- 
pearance in a definition afterwards. Again, as 
every definition properly so called, sets forth dis- 
tinctive marks of the conception defined, it gives at 
the same time the means of dividing or separat- 
ing it from other classes. In order to secure thi* 



312 OUTLINE OF THE 

mutual cooperation, Aristotle lays down, that in 
dividing in order to define, a real genus should be 
taken, to which the differences should be added in 
regular order ; that every dividing species should be 
enumerated; and that each new difference should 
be founded upon, and divide, the foregoing one 
(6La(popai diacpopuv) — thus, it would be better, after di- 
viding bodies into living and not living (p. 105), to 
subdivide living bodies into those which have senti- 
ent life, and those without it, rather than into ter- 
restrial and aquatic, which would have nothing to 
do with the former difference.* 



§ 129. Subordinate Parts of a Science. 

Judgments that relate to speculation only, are 
called theoretical ; those which refer to practice are 
practical. Judgments that require or admit of proof, 
are called demonstrable ; those which are manifest 
from the very terms, are indemonstrable. Thus 
much being premised we can define certain subor- 
dinate parts of a science. 

An Axiom is an indemonstrable theoretical judg- 
ment. A Postulate is an indemonstrable practical 
judgment. A Theorem is a demonstrable theoreti- 
cal judgment. A Problem is a demonstrable prac- 
tical judgment. A Thesis is a judgment proposed 
for discussion and proof (but with Aristotle it some- 
times means an axiom of some special science or 
disputation). An Hypothesis is a judgment pro- 
visionally accepted as an explanation of some group 
of facts, and is liable to be discarded if it is found 
* See An. Post. ii. xiii. 7 (97, a.) ; Met. vii. 12, (1038. a ) 



LAWS OF THOUGHT. 313 

inconsistent with them. A judgment which follows 
immediately from another, is soaietimes called a 
Corollary or Consectary. One which does not prop- 
erly belong to the science in which it appears, but is 
taken from another, is called a Lemma. One which 
illustrates the science where it appears, but is not an 
integral part of it, is a Scholion. 

§ 130. Categories. 

Whilst pure Logic neglects the real nature of the 
things it deals with, and attaches to them only a 
formal value, logicians in almost every age have 
endeavoured to form schemes of classification in 
which things should be arranged according to their 
real nature. Logic deals, as we have seen, with 
second intentions, but it has been found desirable to 
make classes for first intentions also. To these 
classes the name of Categories, or as we might 
render it Attributions, has been given ; for whilst 
they are classes of things and not of propositions, so 
that they do not properly attribute any quality to a 
subject, they are constructed with a view to the 
more ready discovery of attributes when required. 
They are intended, like the labelled drawers in a 
cabinet, to be a well-arranged repository of the 
treasures of thought and knowledge, in which they 
may be kept secure and ready for use. Such a 
system of arrangement for things and the attributes 
of things is essentially metaphysical, and if admit- 
ted into Logic at all, must belong to the application 
of it, wherein we employ the pure forms of thought 
to discover the nature of things. 



314 OUTLINE OF THE 

We require of a good system of Categories that it 
provide a place for every simple notion, and thai 
its heads or divisions be specific enough to furnish 
real help in finding the attributes of any subject ; in 
two words, that it be exhaustive and suggestive. 
Tried by this test, such divisions as that into Sub- 
stance, Mode, and Relation, wiU be rejected as com- 
paratively useless ; if complete and exhaustive, they 
are too vague to offer any tangible suggestions. 
Even the more elaborate division of Aristotle is 
open to this charge ; not to dwell upon the accusa- 
tions sometimes made, that it is confused and in- 
complete. He divides words and notions into ten 
classes, viz : Substance, Quantity, Quality, Relation, 
Place, Time, Position, Mode of Being, Doing, and 
Suffering. Trendelenburg finds an exact corre- 
spondence between these and the grammatical di- 
vision of the parts of speech, the first four corre- 
sponding to Substantives and Adjectives, the next 
two to Adverbs, and the last four to the active, 
passive, and neuter Verbs ; but perhaps he pushes 
a good suggestion, that Aristotle sought in lan- 
guage the groundwork of his arrangement, some- 
what too far. Another important suggestion would 
reduce the number of the principal Categories to 
four. Substance, Quantity, Quality, and Relation ; 
of the last of which the remaining six are only 
subdivisions, for Place and Time are the relation 
of things to each other in space and time, and 
the remaining four imply connection with other 
things.* 

* See Stallbaum, Parmenides, Prol. p. 170. For the history of 
Categories see Professor Trendelenhurg' s Geschichte der Kate^orien- 



LAWS OF THOUGHT. 



815 



Another division of Categories may be jush at* 
tempted. 



TABLE OF THE CATEGORIES. 



SUBSTANCK 



f Quantity 



Attribute 



Quality 



^ Relation 



of Time 
of Space 
of Causation 
of Composition 

of Agreement and Repugnancb 
of Polar Opposition 
. of EiNiTi; to Infinite. 



§ 131. Division of the Sciences. 
No subject has attracted more discussion, than 
that of the right classification of the Sciences; on 
no subject, has discussion produced less agreement. 
Some have proposed to classify according to the pur- 
pose to which sciences are to be applied; others 
according to the faculties through which the knowl- 
edge is derived to us. The former would divide 
sciences into theoretical and practical, according as 
speculation or useful application is to be the result 

lehre, and for the Hindu System of Kanflda, see the Appendix to thff 
present work. 



",tl6 OUTLINE OF THE 

"»f each ; but this barren division ends here, as it 
can only be carried further by importing some new 
principle to assist. The latter would be grounded 
on such distinctions as whether a science were 
rational or experimental, and the like. But it is not' 
true that each science has a separate set of faculties 
set apart to its use ; and in the more complicated 
sciences, the whole mind, with all its powers, finds a 
sufficient employment. 

The most natural ground of classification is that 
according to the subject-matter of the sciences. 
Every science is separated from the rest, in virtue of 
its having for its subject some one set of facts and 
laws, bound together by one conception of which it 
can ' give an account. Astronomy is the science 
which takes account of the heavenly bodies. Physi- 
ology, that which has for its study the phenomena 
of life. Descartes was probably the first who 
insisted that sound knowledge should advance from 
the simpler to the more complex phenomena ; and 
in this remark lay the germ of a sound arrangement 
of the sciences, which scarcely however seems to 
have begun to bear fruit before the time of Ampere 
and Comte. The writer last named, whatever may 
be thought of the general tenor of his principal 
work, or of his later aberrations, has thrown much 
light upon the present subject. 

On the principle which Descartes laid down, the 
following would be the order of the principal sci- 
ences ; and it is accepted substantially by the 
principal writers who have attended to this mode of 
arrangement, such as Comte, Isidore Saint-Hilaire. 
and Cournot. Mathematics, or the science of quan 



LAWS OF THOUGHT. 317 

titles, is at oiice the most simple in its elements and 
the most general in its application, entering more or 
less into all the sciences of nature, and constituting 
almost the whole of that which comes next it in the 
order of dependence. Astronomy, or the science of 
the heavenly bodies, is the application of mathemati- 
cal truths to the laws of matter and motion ; matter 
and the motions of material bodies being the new 
conception which belong to this science. Physics, 
being the science, or rather group of sciences, which 
is conversant with the general laws of the world, so 
far as they relate to beings without life or organiza- 
tion, would come next ; and it imports, in addition 
to the conceptions of Astronomy, those of light, of 
heat, of sound, of electricity, of magnetism, and many 
others. Chemistry would rank next, which is the 
science of the decompos^ition and combinations of 
the various substances that compose and surround 
the earth. Next in order of complexity would rank 
Physiology, founded on the additional conception of 
vegetable and animal life. To this would succeed 
Anthropology, or the science of man's nature; and 
to this Social Science, which ascertains the laws 
that govern men when combined in cities and na- 
tions. Each of these departments may be divided 
into many branches ; as Physics into Acoustics, 
Optics, Electricity, and the like ; or Social Science 
into Morals, Politics, Political Economy, Law, and 
the like. 

On comparing scientific works, differences in the 
mode of teaching the same subject become appar- 
ent. In one the pure theory of Astronomy is 
presented ; in another the striking features of its 



318 OUTLINE OF THE 

historical progress as a science, with speculations on 
the historical sequence of the phenomena them- 
selves ; in a third the practical applications of which 
the science admits in respect to the comfort and 
progress of mankind. This threefold mode of treat- 
ment runs through all the sciences ; and in a table 
of them might well be expressed. The classifica- 
tion would thus embody all that is valuable of 
another system of classes, that according to the 
purpose towards which the science was directed. 

A classification which advances on Descartes' 
principle, from the more simple to the more' com- 
plex subjects, which commences from the notions of 
extension and quantity, and proceeds through ma- 
terial things, up to living, intelligent, and moral 
agents, ought to coincide with the order in which 
the sciences themselves have reached maturity. 
And this it certainly does. Mathematics had made 
good its ground when aetronomy was yet in its 
infancy ; physics began to obtain a sure footing 
later than either; whilst the sciences which relate to 
life are still very immature ; and some of the main 
problems of social science are yet matter of contro- 
versy even in our own days. 

There is besides a general correspondence between 
this classification and the order in which the various 
objects of science came into being. The heavenly 
bodies were first appointed their paths in the celes- 
tial spaces ; then the surface of our earth was pre- 
pared for living creatures ; then they were created 
after their kind, and man the last. The social life 
of man grew up last of all, when his race was mul- 
tiplied on the globe ; and ever as new elements 



LAWS OF THOUGHT. 31& 

appear, the conditions of society are being modified 
even to the present time. 

So far, all the sciences enumerated have been such 
as have the visible universe for their subject. But 
the thought of man is not circumscribed by the 
limits even of the universe ; nay, according to the 
celebrated argument of Descartes, it cannot help 
advancing from the futile and imperfect to the idea 
of the infinite and complete Being. The relations 
of the world and of man to this Being is the subject 
of another science, which we may call Keligious 
Philosophy. That our knowledge of this is less 
precise, and more open to dispute on the part of 
others, arises from the nature of the object and the 
kind of evidence we have of it. The knowledge of 
God begins in an inward need of his aid, and ac- 
cording as that is stronger or weaker, will be the 
disposition to discern Him as the Author of the 
universe, and to consider the facts of nature as so 
many manifestations of Him. The evidence we 
have in the other sciences is direct and primary ; 
for it is derived from the direct contemplation by 
the senses of facts offered to them. But the evi- 
dence on which religious philosophy must proceed 
is indirect and secondary : for it turns on the con- 
viction which arises in us from the contemplation 
of our own mind and the universe around us, that 
there must exist something which is neither our 
mind nor the universe, but the external ground and 
source of both. For this reason Religious Philos- 
ophy must take its place, not as one step in the 
series of the sciences, but rather as something paral* 
lei to, yet distinct from, the whole of them. 



320 



OUTLINE OF THE 



We are now in a position to sketch the table of 
the Sciences.* 



CLASSIFICATION OF THE SCIENCES. 



Group. 



Mode of Treatment. 



I. 


Mathematics 


. Theoretical. 


Historical. 


Applied 


II. 


Astronomy 


. Theoretical. 


Historical. 


Applied 


III. 


Physics 


. Theoretical. 


Historical. 


Applied, 


IV. 


Chemistry . 


. Theoretical. 


Historical. 


Apphfd. 


V. 


Physiology 


. Tlieoretical. 


Historical. 


Applied 


VI. 


Anthropology 


. Tlieoretical. 


Historical. 


Applied. 


VII. 


Social Science 


. Theoretical. 


Historical. 


Applied. 



Eeligious Philosophy. 



§ 132. Conclusion. 

These hints may be sufficient to guide a student 
in applying the principles of Pure Logic to the prac- 
tice of analysis.f 

If this little work is hastily examined and cast 
aside, of course the reader will not have become a 
logician ; he will have learnt the unimportant fact 

* The number of writers on the Classification of the Sciences is 
very great. In drawing up the present section, I have derived as- 
sistance from the works of Comte, Ampere, and Isidore Saint-Wdaire. 
The plan of M. Cournot I only know through the last-named writer ; 
the threefold mode of treatment belongs to his arrangement. Be- 
sides these have been consulted Dr. WheiveU's works, Weise's Archi- 
ttctonick, and a Tract on the subject by Mr. George Ramsay. 

t They are not intended to supersede a reference to such works 
as Whewell's Inductive Sciences, Herschel's Preliminary Discourse, 
and Mill's Logic; to induce the reader to carry his researches on to 
these and similar productions is their chief object. These writers 
have allotted a larger space for the most part to the special sciences 
and their history than was compatible with the present attempt, 
even if sufficient learning and abihty had been at command. 



LAWS OF THOUGHT. ' 321 

that upon this or that disputed doctrine the author 
held this or that opinion, and his knowledge will go 
no further. Instead of learning Logic, he wiU know 
an insignificant fact in logical history. The mistake 
is not uncommon ; — ^we inquire what Aiistotle and 
Bishop Bntler said on morality, and think that we 
have studied Moral Philosophy ; we read the Or- 
ganon, and call ourselves logicians. History presides 
over these and other facts ; we are in lier domain 
when we use our books in this narrow spirit. Phi- 
losophy does not exist until the mind of the student 
begins to work for itself with the principles it re- 
ceives historically ; to decompose and to compose 
anew, to criticize the arguments employed, to essay 
at least to push the confines of truth farther into the 
wilds and error of ignorance, and to leave her a 
j(/ider territory. 

If Grammar is learnt by speaking and writing, if 
a man cannot become an orator without repeated 
efforts to speak in public, nor a poet without prac- 
tising the mechanism of verse till he can use it with 
ease, it seems absurd to expect that a course of lec- 
tures heard, with a string of definitions learnt, will 
make a logician. 

Let those who wish to possess the intellect they 
have received from above, in the depth and clear 
ness, the sober composure, the calm activity which a 
high degree of culture can alone bestow, venture to 
study Logic in a larger spirit than the merely his- 
torical. Let them become dialecticians ; not in the 
sense which the sophist attached to that name, but 
rather in that which the scourge of sophists gave it. 
Let them not use so excellent a weapon as the rea« 

21 



322 OUTLINE OF THE LAWS OF THOUGHT. 

Bon in mere play, with a guarded point and bated 
edge, but let them keep it sheathed, sharpened, and 
shining, till a battle has to be fought against an 
error. Let them watch for themselves the processes 
gone through in completing any science. If the 
rules given in books are erroneous, let them try to 
correct; if imperfect, to complete them: or if expe- 
rience verifies their truth and utility, let them be 
regarded with a degree of trust greater than could 
have been awarded to them before, when they stood 
in books, the mere historical record of other men's 
philosophy. No one who has studied Logic in this 
conscientious spirit has ever found it trifling or use- 
less. 



APPENDIX. 



S INDIAl^ LOGia 



ON INDIAN LOGIC* 




HE sciences of Logic and of Grammar were, as far as 
history allows us to judge, invented or originally cou' 
ceived by two nations only, by Hindus and Greeks. 
All other nations, if they ever cultivated these scien- 
ces, received the first impulse from without. The 
Romans from the Greeks, the Germans from the Romans, the Arabs 
from the Greeks, the Jews from the Arabs. 

That the two most highly gifted nations of the world, the Hindus 
and the Greeks, should both have been led, each in its own way, to 
a study of the laws of thought and the laws of language, seems in 
itself perfectly natural. 

At the time, however, when the different systems of Hindu philos- 
ophy became first known to the scholars of Europe, at the beginning 
of this century, every thing that came from the East was looked 
upon as of extreme antiquity.- There had been vague traditions of 
Indian philosophy long before the time of Aristotle. There were 
reports of early Greek sages travelling to India as the fountain-head 
of ancient wisdom. Alexander himself had found himself in India 
face to foce with a whole nation of philosophers. It was readily ad- 
mitted, therefore, that the Hindii system of Logic was more ancient 
than that of Aristotle, and that the Greeks borrowed the first ele- 
ments of their philosophy from the Hindus. Alexander, who had 
been himself in conversation with the Logicians of India, might have 
sent some of their treatises to his tutor at home, and Aristotle would 
have worked them up into a system of his own. This view was 
actually taken and defended by men like Gorres.f They were struck 



* Communicated by Professor Max Wiiller. 

t GoiTes undertook to prove that the Greeks had borrowed some techni- 
cal terms from the Sanskrit. Indian philosophers admit five elements, and 
the fifth is called nkds, ether. This ether has quite a different meaning 
from the aWfjp which some Greek philosophers considered as the fifth or 
highest element. Gcirres, however, quotes f-.rithout giving a reference) » 



326 APPENDIX. 

by many points of coincidence in botli systems of Logic. In each 
there were Categories, Genus, and Species, and even Syllogisms ! 
It could not be otherwise — the Greeks must have borrowed it from 
the Hindus. That two nations, if they once conceived the idea of 
analj^zing tlie laws of thought, could possibly arrive at similar re- 
sults even on the most general points, and tliat it would require coin- 
cidences in many minute details or in palpable errors, to prove beyond 
doubt that the two systems had a common origin, seems never to 
have occurred to these enthusiastic Orientalists. 

But on the other hand, does it show a higher power of logical rea- 
soning or historical criticism, if we find men like Niebuhr taking the 
opposite view of the matter, and deriving Indian philosophy from 
Greece ? Niebuhr is reported to have said in his Lectures on An- 
cient History, " If we look at Indian Philosophy, we discern traces 
of a great similarity with that of the Greeks. Now as people have 
given up the hypothesis, that Greek philosophy formed itself after 
Indian philosophy, we cannot explain this similarity except by the 
intercourse which the Indians had Avith the Grseco-macedonic kings 
of Bactra." 

To Niebuhr and to most Greek scholars it would naturally be next 
to impossible to believe that Greek Logic and Greek philosophy in 
general were of foreign origin and a mere importation from India. 
They know how Greek philosophy grew up gradually, how its course 
rims parallel with the progress of Grecian poetry, art, and civilizar 
tion. They know that it is a home-grown production as certainly as 
that Plato and Aristotle were Greeks and not Brahmans. 

But, then, a Sanskrit scholar has just the same conviction with 
regard to Indian philosophy. He can show how the first philosophi- 
cal ideas, though under a vague form, existed already in the mind of 
the early poets of the Veda. He can trace their gradual develop- 
ment in the Brahmanas and TJpanishads. He can show how they 
gave rise to discussions, how they took a more distinct form, and 
were at last fixed and determined in the most scientific manner. He 
+00 is as certain that Indian philosophy was a native production of 
India, as that Gotama and KanAda were Hindus and not Greeks. 

Until, therefore, it can be proved historicaUij that Greeks received 
tlieir philosophy from India or Indians from Greece — or until coinci- 
dences can be pointed out which it is impossible to explain otherwise, 
it will be best to consider both Greek and Indian philosophy as au- 

passage from Aristotle, where this fifth element is mentioned under tho 
name of aKOT-ovo/iaTOV, and this he translates by " akas-nominatum,"— • 
&KOT-ovcfiaTov being evidently an ingeiiors conjecture for aKaT0v6fia(JT0v. 



ON liMDIAlS LOGIC. 327 

tochthonic, and to derive from their /nutual similarities only this 
consolatory conviction that in philosophy also there is a certain 
amount of truth which forms the common heirloom of all mankind, 
and may be discovered by all nations if they search for it -with hon- 
esty and jDerseverance. 

According to the accounts which the Brahmans themselves give 
of the history of Indian philosophy, there have been, and there still 
exist, six systems of philosophy. They are called the Sankhya, 
MimSnsa, Nyaya, Yoga, Vaiseshika, and Vedanta. These systems 
are not represented to us in a successive order, tliey do not apparently 
arise one upon the ruins of the other, like the schools in the history 
of Greek and German philosophy. They always seem to run paral- 
lel, each maintaining its place side by side with the others, and each 
representing a distinct view of the Universe, and of the relation of 
the seeming to the real world. Even at the present day the Brah- 
man unites three or more of them in his course of study. 

Each of these systems is complete in itself. Each contains some- 
thing of what we should call Physics, Metaphysics, Logic, and even 
Ethics. In one system, however, certain topics occupy a more prom- 
inent place and are discussed at greater length. Thus, while the 
Mimansa is more theological, and the bankhya more metaphysical, 
the Nyiiya system, in which the reasoning faculties of man are more 
closely examined, has become known to us by the name of " Indian 
Logic." In India also, a Naiyayika, or follower of the Nyiya, means 
as much as a Logician, or a man who understands the laws of rea- 
soning, and still more the art of logical wrangling. The other sys- 
tems refer to the Nyaya, whenever logical questions have to be set- 
tled. 

Nevertheless, it would be wrong to call the Nydya, Logic, in our 
sense of the word. The Ny&ya, as well as the other systems, has for 
its highest object the solution of the problem of existence, and only 
as a means towards accomplishing this object, does it devote particu- 
lar attention to the instruments of knowledge — and, as one of them, 
to syllogistic reasoning. 

In order to explain what in the mind of a Hindu philosopher would 
correspond to our Logic, it Avill be necessary to give a short sketch 
of the Nyaya. We shall there see the exact place which Logic oc- 
cupies in the system of Hindu philosophy, and be able to judge how 
far it corresponds to that which Aristotle and other philosophers after 
him have assigned to this philosophical discipline. The reason why 
the Ny&ya is chosen in preference to other systems, is not because it 
alone contains an account of the syllogism. The syllogism finds its 
place in the Vedanta and S&nkhya as well ; but it is more fully treated 



328 APPENDIX 

by the Naljayikas. Again, Ka«uda's work, called the Vaiseshika 
philosophy, is chosen in preference to the Nyaya-sutras of Gotama, 
because tliere is so much of minute technicality in the latter^ that it 
would be very difficult to give a complete account of it in a short 
compass. 

KanUda starts boldly by declaring that he is going to explain how 
a man can obtain the most exalted and exalting knowledge of reality, 
and by means thereof arrive at a state of complete blessedness, the 
Summum Bonum. The way to blessedness, according to him, is 
knowledge, but knowledge of a particular kind, that is to say, a dis- 
criminating knowledge of the seven * Categories. 

These Categories are, Substance, Quality, Action, Genus, Individ- 
uality, Concretion, and Non-existence. 

The Sanskrit word which has been translated by category is " pa- 
dartha," which in common usage means a thing. The etymological 
signification, however, is " meaning of word," which, if interpreted 
philosophically, comes to express " the most general meaning of 
words," " what is common to all words," what is predicated by 
words without any regard to their special meaning, as given in the 
Dictionary. Like the Categories of the Greek system, the Padilrthas 
are wide classes of " first intentions." They are the last and highest 
predicates, and tlie only thing that can be predicated of them accord- 
ing to Visvanatha, is their " perceptibility." 

But does this perceptibility involve their reality ? "We must hear 
the objections which the Hindu Materialist raises against this sup- 
position. Taking the first category, that of substance, he says, "All 
we really perceive, if we speak for instance of water, is water. We 
do not perceive any thing of water being a substance. Therefore 
you have no right to speak of substance as a category." But, an- 
swers the Vaiseshika, though we do not perceive substance with our 
eyes, yet we perceive that there must be something in which qual- 
ities can reside; something which remains unchanged though the 
qualities change ; — which rests the same whether it becomes a cause 
or an effect. This then we call substance. 



* Originally there were but six, Non-existence being omitted in Kanada s 
Sutras. The statements given here are taken from Annambha^ia's Tarksi- 
sangraha, published at Benares withoiit the name of the editor. This pub- 
lication, and many most valuable works lately issued from the Sanskrit 
College of Benares, are due to Dr. Ballantyne, the Principal of this Col- 
lege. A Hindostani translation, together with an English translation, waa 
also published at Benares, from the hand of Mr. F. Edward Hall, though 
without his name 



ON INDIAN LOGIC. 329 

Quality, again, is what resides in a substance. Quality itself baa 
no qualities, but substance has. 

Quality produces by itself no change. What produces change, or 
combination and separation of qualities, is what we comprehend 
under the third Category, or Action, and this also resides in sub- 
stance only. 

These are the three principal categories, and they seem to cor- 
respond very nearly with Aristotle's ovala, ttolov and noaov, and 
TvoLeZv. After these three, follow the two categories of Genus and 
Individuality. 

Genus resides in Substance, Quality, and Action, and it is twofold, 
higher or lower. The highest genus, which is shared by every thing, 
is " being," the summum genus. Next to it we get as lower genus 
that of being a category, of being substance, earth, a clod, &c. 

Individuality is endless. It resides in substance only, and as we 
shall see, in substance before it becomes material and perceptible by 
the senses, that is to say, in atomic substances. Individualities mu- 
tually exclude each other. 

The next category stands as it were by itself, and forms the top 
of the pyramidal arrangement of the categories, which tapers fi'om 
the fundamental three, to the qualifying two, and ends in that which 
we translate by " Concretion." It is peculiar to Indian philosophy 
and difficult to be rendered into the philosophical language of 
Europe. It expresses the intimate relation of things which cannot 
exist separately. A quality, for instance, cannot exist by itself, but 
only as the quality of a substance, nor can substance exist except 
with reference to qualities. Now, substance and quality are not 
considered as merely together, but as interwoven, as inseparable, 
and mutually dependent ; and this relation is expressed by the 
category of Concretion. The same relation exists between the 
whole and its parts, between Genus and Species, between cause 
and effect. 

The last category, Avhich, as we saw, is omitted by some of the 
Vaiseshikas, is that of Non-existence. It is of four kinds, according 
as it applies to things : 1. Which are not yet, but may be after- 
wards ; 2. Which are no more, but have been ; 3. Which are not, 
and never will be ; 4. Which are not what something else is, i. e. 
which differ. 

Of these seven categories, which exhaust the universe of knowl- 
edge (omne scibile), Substance comprehends the five elements, 
earth, water, light, air, and ether; it comprehends time and space j 
soul and self. 
The five elements may be either eternal, uncreated not percep 



330 APPENDIX. 

tible by the senses, but established by inference ; or created, per- 
ceptible and destructible. In the former state they exist as infinitely 
small, in the latter they are products. Considered as products again, 
the elementary substances are threefold : organic, organ, or inor- 
ganic. Earth, which is determined as that which has the quality 
of Odour, exists, as organic, in animal bodies. As organ it is the 
apprehender of odour. As inorganic it consists in stones. In this 
manner we get five organs : the organ of hearing corresponding to 
the substance of ether ; that of feeling to the substance of air ; that 
of seeing to light ; that of tasting to water ; that of smelling to earth. 
Ether has one quality, and the organ of hearing apprehends one 
quality, that of sound. Air has two qualities, and the organ of 
feeling apprehends two, those of sound and tangibility. Light has 
three qualities, and the organ of sight apprehends three, those of 
sound, tangibility, and colour. Water has four qualities, and the 
organ of taste apprehends four, those of sound, tangibility, colour 
and savour. Earth has five qualities, and the organ of smell ap- 
prehends five, those of sound, tangibility, colour, savour, and 
odour. • 

Here then we have something very like the doctrine of Em- 
pedocles, 

Tairi iJ£V yap yalav bnu^xajiev, vSarc 6' rik.'p, 
AldepL 6' alMpa dlov, urop TTvpl nvp at6r/?i,ov, 
2rop}'?/v 61 CTopyri, vsiKog (5e re veIksi ?ivypu), 

only carried out to too great an extent, and thereby caricatured. 
The only remark which it is necessary to make, is that "ether" is 
treated differently from the other elements. "While the other four 
elements exist both in an atomic and in a terrestrial state, ether 
never leaves its transcendental reality, but is eternal, one, and in- 
finitely great (all-pervading). 

The next two substances, which, like ether, exist as eternal only, 
as one and all-pervading, are Time and Space. Time is the cause 
of what we call Past, Present, and Future. Space is the cause of 
what we call East, West, North, South, &c. Both time and space 
being eternal substances, and eternal only, it follows that they are 
never perceptible by. the organs of the senses. 

The eighth substance is Self. It is the substratum of the qualities 
of knowledge, wish and will. It is twofold, the living Self and the 
Supreme Self The Supreme Self is the Lord, the Omniscient ; He 
is One only, free from joy and sorrow. The living Self is attached 
to different bodies, but it is still eternal and all-pervading. Wherever 
the body is, there is the living Self; but the living Self itself remai:iJ 



ON INDIAN LOGIC. 331 

luiereated ami eternal. Its existence can be proved, but it cannot 
fall under tlie cognition of the senses. 

The last substance is Soul, the cause of perception, of pleasure 
and pain, and the passions. As Self, though attached to bodies, i? 
all-pervading and infinite, we should not be able to account for the 
fact of our successive or discursive knowledge. Self, like the Om- 
niscient, would know every thing at once, unless there was the soul, 
through which all impressions must pass in succession and become 
individualized. Soul, too, is eternal only, but it is endless ; — not in- 
finitely great, but infinitely small, and attached, not to the Supreme, 
but to living Selves only. 

It is not necessary to enter into a more detailed account of the 
substances, for it is clear that there is onlj^ one Substance which will 
fall under our more immediate consideration, the Substance of Self, 
and this only as the substratum of the quality of knowledge. It is 
where the quality of knowledge is examined, that we shall recognize 
what by European philosophers is treated as Logic. 

Before we proceed, however, to that Chapter, we must at least 
cast a glance at the different headings of the two categories of quality 
and action. 

Qualities are, 1. Colour; 2. Savour; 3. Odour; 4. Tangibility; 
5. Number; 6. Dimension; 7. Distinction; 8. Conjunction; 9. Dis- 
junction; 10. Priority; 11. Posteriority; 12. "Weight ; 13. Fluidity; 
14. Viscidity ; 15. Sound ; 16. Perception ; 17. Pleasure ; 18. Pain ; 
19. Desire ; 20. Aversion ; 21. Effort ; 22. Merit ; 23. Demerit ; 
24. Eaculty. They are eternal if residing in eternal substances, 
and non-eternal if residing in material bodies. Knowledge, Pleasure 
and Pain, Desire and Aversion, Effort, Merit and Demerit, are qual- 
ities of the Self only. Perception, Desire, and Effort are eternal as 
qualities of the Supreme Self, but non-eternal as qualities of living 
Selves. 

Actions are, Lifting up, Throwing down. Contraction, Expansion, 
and Procession. They exist only in the four elements and in 
Sold. 

The fourth Category, or Genus, is something which resides in 
substance, qualities, and actions, but is eternal, and as such not 
sensuously perceptible. It is one, but it always resides in many. It 
is that by which it becomes possible to comprehend several things 
into one class, and to predicate something of them, which they have 
in comlnon. We call this an abstraction ; but to the Hindu the 
Genus of things, or the General, is something real, inherent in sub- 
staace, or quality, or action, though of course not material or per- 
ceptible by the senses. The Genus, therefore, or the cause of what 



332 APPENDIX. 

we call general, is conceived as something independent of single 
objects, though it is known to us only as inherent in the objects of 
intuition. It is inherent in substances, qualities, and actions, and is 
perceived by us as we perceive either substances, actions, or qual- 
ities. What Ka«ada means by calling Genus inherent, is that sub- 
stances, qualities, and actions cannot exist, not even in their eternal 
state, without the Genus. The same applies to Individualities, only 
that they do not inhere in qualities and actions, but in substances 
only. Individuality is what makes a thing to be itself, and not any 
thing else. And if we hear IvaHada expressing his opinion, that " in- 
dividualities which mutually exclude one anotlier, exist in substances 
only," wc almost seem to read the words of Aristotle, to tI ecmv 
dw^xJc Ty ovcia vTTupxsi. 

These five categories would apparently exhaust the meaning of 
every word (padartha). If we take, for instance, the Avord lightning, 
and ask Kanada what is expressed by it, he would say, first, a sub- 
stance, and more particularly, an elementary substance. Secondly, 
a number of qualities, like colour, distance, or dimension. Thirdly, 
action, and here the action of throwing down, which cannot be a 
quality, because qualities are always conceived as at rest. Fourthly, 
a genus ; because when we speak of lightning, we imply that it 
exists not once only, but as a class, which class is a lower genus if 
compared with light. Kfthly, an individuality ; because we mean 
this particular lightning, which never existed before and never wiU 
exist again. Nevertheless, says Ka^ada, these five categories do not 
yet contain all that we mean by the word lightning. It is not the 
mere agglomerate of substance, quality, &c. that constitutes a real 
conception — but these categories must again be intimately connected 
or interwoven, before they i-epresent or constitute a reality. The 
juxtaposition of categories would be a mere abstraction, and it 
requires the category of concretion to make aU the other categories 
concrete and real. With it, we predicate, not, first substance, then 
quality, and so on, but we predicate substance as necessitating 
quality, quality as inseparable from substance, genus inherent in 
both, and individuality supported by genus. Thus only does a real 
conception become fully exhausted by categorical analysis. 

AYe now return to a consideration of the qualities, and more especi- 
ally of that which is called "Knowledge." Knowledge is a quality 
of the Self in the same manner as colour is of light. It is inseparably 
connected with it, and is explained as the cause of every coneeption 
that is expressed in language. Knowledge is either '•emembrance or 
perception. Perception is twofold, right or wrong. Eight percep- 
tion represents the thing such as it is, silver as silver. This is called 



JN INDIAN LOGIC. 333 

tnith (pramA). Wrong perception represents the thing as the thing 
is not, mother-o'-pcarl as silvtr. 

Eight perception is fourfold, sensuous, conclusive, comparative, 
and authoritative. It is produced by the senses, by inferring, by 
comparing, and by revealed authority. Tliis fourfold division of 
knowledge is taken from Gotama and not from Kawada. Ka/iada 
admits but two sources of knowledge, perception (pratyaksha) and 
inference (laingika) ; that is to say, he comprehends all knowledge 
which does not arise from the senses, under the general title of in- 
ference. The different systems of Hindu philosophy have been 
arranged by Colebrooke, according to what each considers to be the 
only trustworthy means of knowledge. The A'arvaka or Materialist 
admits but one source of knowledge, sensuous perception. The 
Buddhist and the Vaiieshika admit two, perception and inference. 
Manu (xii. 105) and Sankhya philosophers admit three, for they ac- 
knowledge, besides perception and inference, the authority of reve- 
lation. The followers of Gotama add comparison as a fourth instru- 
ment of knowledge ; the Prabhakaras presumption as a fifth, and the 
MimAnsakas privation or negation as a sixth. To the Self it is in- 
different whether its knowledge is produced by any one of these 
instruments, as long as each represents the thing such as it is. 

We pass over the chapter on causation, which serves as an intro- 
duction to the chapter on sensuous perception. Nor do we enter into 
the intricacies of sensuous perception, of which six different kinds 
are enumerated and explained. They arise from the different ways 
in which the organs of sense are brought into contact with their 
objects, which objects may be either substantial matter, or qualities 
and actions, as inherent in substance, or the Genus, as inherent in 
substances, qualities, and actions. 

After sensuous knowledge comes conclusive knowledge, which is 
gained by means of inferring. Conclusive knowledge is, for in- 
stance, " This mountain is a volcano," whereas our sensuous per- 
ception is only that the mountain smokes. In order to arrive from 
this at the conclusion that it is a volcano, we must be in possession 
of what is called a pervading rule, or a Vyftpti. This pervading 
rule, which sometimes might be called a law, is, that smoke is in- 
separably connected with fire, or, as the Hindu calls it, that smoki- 
ness is pervaded by fieriness, that wherever there is smoke there is 
fire. If we possess this Vyapti, which we may remember by such 
instances as a culinary hearth, &c. then, in order to arrive at conclu- 
sive knowledge, we only require consideration (parAmar^a) in order 
to find out in any sensuous impression something which can bo 
pervaded, something which can make the mountain the membel 



834 APPENDIX. 

(patsha) of a VySpti, this something being, in our case, the smoke. 
If we know that the smoke which we perceive, is quahfied to become 
part of a VyApti (this Vyapti being, " wlierever tliere is smoke thwe 
is fire "), then we know conclusively that this mountain is fiery, be- 
cause it smokes. 

It would have been easy to translate these definitions into more 
technical language. We might have clothed Kan&da in a Grecian 
garb, and made him look almost like Aristotle. Instead of saying, 
that conclusive knowledge arises from a consideration that there is 
something in an object which is pervaded by something else, and 
that the pervading predicate is predicable of all things of wliich the 
pervaded predicate is, we might have said, the conclusive knowledge 
that S is P, arises from the consideration that S is M, and M is P, or 
with Aristotle, 6 avTiXoyca^br Sia tov fiiaov to uKpov ru TpiTcj6ciKwaiv. 
What Kanada calls member of a pervasion (paksha, e. g. mountain), 
we might have translated by subject or terminus minor ; what per- 
vades (vycipaka or sadhya, e. g. fieriness), the predicate or terminus 
major ; and what is to be pervaded (vyapya, e. g. smokiness), the 
terminus medius. But what should we have gained by this 1 All 
that is peculiar to Indian philosophy would have been eliminated, 
and what remains would have looked like a clumsy imitation of 
Aristotle. Multajiunt eadem seel aliter, audit is this "aliter" which 
constitutes the principal interest in a comparative study of philosophy. 
Even such terms as conclusion or syllogism are inconvenient here, 
because they have with us an historical colouring, and throw a false 
light on the subject. The Sanskrit Anumana is not avfinipaGfia, but 
it means "measuring something according to something else." This 
is done by means of "paramarsa," which means "groping," or try- 
ing to find in an object something which can be measured by some- 
thing else, or which can become the member of a pervasion. This 
corresponds to the discovery of a terminus medius. In Kapila's 
system (I. 61), the principal object of inference is said to be tran- 
scendental truth. Things which cannot be seen with our eyes, are 
perceived by inference, as fire is from smoke, and he defines infer- 
ence (I. 101) by "knowledge of the connected, arising from percep- 
tion of a connection or a law." But, again, the relation of what 
pervades and what is pervaded is Yery different from what we .should 
call the relative extension of two conceptions. This will become 
more evident by what follows. For the present we have learnt, tliat 
the act of proving (anumana) consists in our knowing that there is 
on the mountain fire-pervaded smoke. Through this we arrive at 
anumiti or conclusive knowledge, that tlie mountain is a volcano. 

What follows is translated from Aunambha«a's Compendium 



O^q INDIAN LOGIC. 335 

" The act oi concluiling is twofold, it being intended either for one's 
own benefit or for others. The former is tlie means of arriving for 
ones's self at conclusive knowledge, and the process is this. By repeat- 
ed observation, as in tlie case of culinary liearths and the like, we have 
obtained the general rule (vyapti), that wherever there is smoke there 
is fire. We now approach a mountain and wonder whether there 
might not be fire in it. We see the smoke, remember the general 
rule, and immediately perceive that the mountain possesses fire-per- 
vaded smoke. This is, as yet, called only groping after signs (linga- 
parAmarsa). But from it arises the conclusive knowledge, that the 
mountain itself is fiery. This is the actual process when we reason 
with ourselves." 

" If we try, however, to convince somebody else of what we know 
to be conclusively true, then we start with the assertion, The moun- 
tain is fiery. Why 1 Because it smokes ; and all that smokes, as 
you may see in a culinarj' hearth and the like, is fiery. Now you 
perceive that the mountain does smoke, and hence you will admit 
that I was right in saying, tliat the mountain is fiery. This is called 
the five-membered form of exposition, and the five members are sev- 
erally called, 1. Assertion, tlie mountain has fire ; 2. Reason, because 
it has smoke ; 3. Proposition, all that has smoke lias fire ; 4. Assump- 
tion, and the mountain has smoke ; 5. Deduction, therefore it has 
fire. The means of inference in both cases is the same. It is what 
was called the groping after signs, or tlie handUng of the demonstra- 
tive tokens, in which the essential process of inferring consists." 

What is called by Annambhaf/a the conclusion for one's self corre- 
sponds totidem verbis witli the first form of Aristotle's syllogism : 

All that smokes is fiery. 
The mountain smokes ; 
Therefore the mountain is fiery : 

What is called the conclusion for others seems more irregular, on 
account of its five members, and of the additional instances, which 
seem to vitiate the syllogism. 

We must not forget, however, that whatever there is of Logic in 
these short extracts, has but one object, that of describing knowledge 
as one of the qualities of the Self. Knowledge, as KawAda has 
eliGwn, is not confined to sensuous perceptions, and therefore knowl- 
edge gained by inference is examined next. The question is, how is 
it that we know ajiy tiling beyond what we perceive with our senses? 
The answer is, by inferring. If we place ourselves on this point of 
view, wliich KajiAda has taken, it becomes clear, first, that we cannot 
expect from Ka/jada a treatise on formal Logic. The formal Logician 



336 APPENDIX. 

takes a purely scientific interest in the machinery of the human 
mind He collects, arranges, and analyzes the functions of our rea- 
soning faculties, as they tall under his observation. But the question 
which occupies Kanlda is, how is it that we know things which we 
do not see, and how can we prove that we do know them ? Now the 
instrument by which we know things which we do not perceive with 
our senses, is inference. Hence, Kanada has to explain first, what 
inference is, and how we do infer ; secondly, hoAv far inference can 
be made to yield the same certainty as our sensuous impressions. 
For this purpose, it seems that neither the deductive nor the induc- 
tive syllogism, if taken by itself, would have been sufiicient. Deduc- 
tive reasoning may in itself be most valuable for formalizing facts, it 
may give a variety of different aspects to our knowledge, but our 
knowledge will never be substantially increased, no new fact will ever 
be discovered by it. And if on one side Kawada cannot use deduc- 
tion because it teaches nothing new, he cannot use induction either, 
at least not in its general acceptation, because it teaches nothing cer- 
tain. 

The only object of all knowledge with Ka?iada, as we saw before, 
was absolute truth, or prama. Now Aristotle does not make a secret 
of it, that the eTvayuyfj, in order to prove the cAuf, must be 6id Tzdv-uv, 
and that this is impossible. Knowledge gained hy epigogic reason- 
ing is, strictly speaking, alwaj's em to Tioh'i, not what Ka^i'ida would 
call prama. The conclusion which Aristotle gains by way of induc- 
tion, " Animals which have little bile are long-lived," might be called 
a Vyapti. Aristotle arrives at this, by saying, man, horse, and mule 
(C) are long-lived (A) ; man, horse, and mule (C) have little bile 
(B) ; therefore all animals with little bile are long-lived. But Ka«&- 
da would express himself in a different way. He would say, wher- 
ever we perceive the attribute of little bile, we also perceive the attri- 
bute of long life, as, for instance, in men, horses, mules, &c. But 
here he would not stop, but he would value this vyapti merely as 
a means for establishing a new fact ; he would at once use it as a 
means of deduction, and say, " now the elephant has Mttle bile, there- 
fore is he long-lived." 

One thing can be said in favour of the Indian method. If we go 
on accumulating instances, as in the case before mentioned, if we add 
horses, mules, men and the like, we approximate more and more 
towards a general rule, hut we never eliminate real exceptions, not to 
speak of possible exceptions. The Hindii, on the contrary, by say- 
ing, " Wlierever we see the attribute of little bile, we observe long 
life," and then giving a number of instances b\' way of illustration, 
excludes the reality, though he does not exclude the possibility, of 



ON INDIAN LOGIC. 337 

exceptions. He states it as a fact, that wherever the one has been, 
there has been the other, which throws the onus probandi as to a case 
to the contrary, upon the other side. In our system, there is nothing 
to force an opponent to admit a hundredth case, because in ninety-nine 
cases the rule happened to be true — while, if it is impossible to attack 
the "Wherever" of the Hindu, there is in this Wherever a real 
power that brings conviction for every case that comes under it. If 
it can be proved that there never was an instance where smoke was 
seen without fire, the mutual inherence and inseparable connection 
of smoke and fire is established more stringently than by any num- 
ber of accumulated instances where the two have been seen together. 
The conditions under which it is allowed to form a VySpti, that is to 
say, to form Universals, have occupied the attention of Hindu phil- 
osophers more than any other point in Logic. They distinctly exclude 
the mere accumulation of observations. For things, they say, may 
be together a hundred times, and may still not be mutually inherent. 
They make exceptions for practical purposes. There repeated ob- 
servations may be turned into a general rule, but not in philosophical 
discussions. Volumes after volumes have been written on this sub- 
ject, and though I do not beheve they will throw new light on the 
question of the origin of Universals, yet they would furnish a curious 
parallel to the history of the European Intellect. 

It will be necessary, before closing these remarks, to say a few 
words in answer to the attacks which have been made on Indian 
Logic. 

It has been said that the instances which occur in the third mem- 
ber of the five-membered argument, vitiate the conclusion. The 
proposition that wherever there is smoke there is fire, was supposed 
to lose its universal character if it was followed by an instance, " as 
in the culinary hearth." Against this we have to remark, first, that, 
according to Hindu logicians, this instance is not essential, and is 
therefore occasionally left out altogether. Next, the instance is never 
used to confirm the universal proposition, but to illustrate it, and for 
this very reason it is chiefly used in rhetorical inductions. From the 
Sutras of Gotama (I. 35), it might certainly appear, as if the object 
of the third member was to give an instance. He says, " the propo- 
sition, or the third member, is an instance which, from tlie fact that 
emoke accompanies fire, shows that fire must be there." However, 
the Commentator explains that this is not strictly a definition of the 
third member, but merely an explanation; What the third member 
Bupplies is a statement that fieriness pervades smokiness, together 
with an example to make the connection between them more appar- 
ent. 

22 



338 APPENDIX. 

In the original -vrork of Kanada, of which tlie Library of the East 
India House possesses a MS., containing text and commentary, we 
see still more clearly that the third member is simply an universal 
proposition. We read there (p. 76, a.) : " Inference is twofold, either 
for one's self or for others. That for others consists of five sentences, 
which are called Assertion, Reason, Proposition, Assumption, and 
Deduction. Assertion does not mean more or less than the wording 
of the conclusive knowledge which is to be established. Eeason is 
that member which expresses in the ablative the means of proof 
Proposition is the third member, which shows that the means of 
proof and what has to be proved by it, are never one without the 
other. The Assumption shows that the means of proof (heretofore 
determined as inseparable from what is to be proved) belongs to the 
subject of our assertion. And the Deduction shows that therefore 
what is to be proved belongs to the subject. The argument there- 
fore proceeds in the following way, A word is non-eternal, because 
it is composed ; whatever is composed is non-eternal ; a word pos- 
sesses the quality of being composed, such quality being pervaded 
by non-eternity; therefore a word is non-eternal." He further 
states that the names of the five members mean with the Vaise- 
shikas, Promise, Pretext, Authority, Scrutiny, and Repetition. 

In Ka7iada's system, therefore, it would seem as if the instance, 
belonging to the proposition, was altogether ignored, and we might 
feel inclined to admit that it occurs only incidentally in Gotama's 
philosophy. But if we inquire more carefully, we find that the 
instance in Gotama's syllogism has its own distinct office, not to 
strengthen or to limit the universal proposition, but to indicate, if I 
may say so, its modality. Every Vyapti must, of course, admit at 
least one instance. These instances may be either positive only, or 
negative only, or both positive and negative. If it is said, " The 
jar is nameable, because it is knowable ; every thing that is know- 
able is nameable ; " we can only have positi\ e instances, as tree, 
table, and the like. It is impossible to bring a negative instance of 
something which is not provable, because every thing is provable. 
On the contrary, if we have a case, like " the earth is different fi-om 
all the other four elements, because it has odour," it is impossible to 
go on — " All that is different from the other elements has odour," — 
because the only case in point would again be " earth." Therefore 
we must here employ the negative VySpti, and say. Whatever is not 
different from the other elements, has no odour, and then it is pos- 
sible to add an instance, namely, water, light, &c. After this the 
Hindi! proceeds, Now earth is not so (not inodorou.';) ; Therefore it 
is not so (not different from the other elements). 



ox INDIAN LOGIC. 339 

Brahmans liave been told by European Logicians that they could 
have all this more cheaply, by saying, " Whatever is odorous differs 
from the other inodorous elements ; " " Earth is odorous ; " " There- 
fore earth differs from the otliers ; " But the Vaiseshika stops us at 
the very first word, he does not admit the " Whatever," because it 
is not a " Whatever," but only one single case. It would be impos- 
sible to give instances, nay, to give a single instance for the VySpti, 
proposed by the European Logicians, except earth over again. 

The third case is, where the Vyapti admits both of positive and 
negative instances, as in the hackneyed syllogism of the volcano. 
Here we can say. Wherever there is smoke, there is fire, as in cul- 
inary hearths and the like. And wherever there is no fire there 
is no smoke, as in the lake. 

So much for the instances added to the third member, which were 
supposed to vitiate the syllogism. 

Still more unfounded is another objection. It w^as said that the 
formalities of the Science of Logic were perfectly satisfied with three 
out of the five members of the Indian syllogism. Of course they 
are, and the Hindus knew this 2000 years ago. We have seen that 
the five-membered method was employed when a person, after 
having himself arrived at conclusive knowledge, wished to persuade 
somebody else of the truth of his belief. Now, if " the sole object 
of Logic is the guidance of our own thoughts, and the communica- 
tion of those to others is under the consideration of Rhetoric," it is 
clear that the scjieme of the five-membered syllogism belongs to 
Rhetoric and not to Logic. Whether or no the five steps as they 
follow one another, according to Ka?jada, represent what does actu- 
ally take place in a wellrconducted argument, we may leave to 
Rhetoricians to decide. But, in order to show that even this far- 
fetched objection would not take the Brahman philosopher by sur- 
prise, we quote the following passage from the Vedanta-paribhSshl : 
"Inference is twofold, intended either for ourselves or for others. 
The former has been explained. As to the latter it is to be accom- 
plished by means of an argument. An argument consists of several 
members. And real members there are only three ; assertion, rea- 
son, proposition ; or proposition, assumption, and deduction. Not 
five ; for three are sufficient to exhibit the pervading rule and its 
two members, the other two can therefore be dispensed with." 
Now, in the first case, which would give us " the mountain is fiery, 
for it smokes, all that smokes is fiery," it must be admitted there 
would be a want of all syllogistic arrangement. The first two mem- 
bers might be called an Enthymema, but then the third would be 
superfluous. But the fact is that Hindu philosophers never use the 



340 A.^PENDIX. 

three members in this succession ; and if they say, that the three 
first are sufficient for a conclusion, they take no account of their 
successive collocation, but simply mean that Proposition, Reason, 
and Assertion would form a syllogism as well as Proposition, 
Assumption, and Deduction. But, although the Hindii Logicians 
admit, in common Avith their brethren in Europe, that a complete 
syllogism consists of three members, they do by no means restrict 
themselves to the use of the three-membered syllogism. Gotama, 
for instance, says there are three kinds of syllogism, from cause to 
effect, from effect to cause, and from the Special to the General. 
Thus we infer that it will rain from the rising of clouds, it has rained 
from the rising of rivers ; we infer that a thing is substance because 
it is earth. But, with the exception of the last case, it would be 
impossible to frame an absolute proposition, or a vySpti, from which 
the deductions could be established. 

So much in answer to objections which have repeatedly been made 
against Indian Logic. I should like to see the Brahmans them- 
selves take up the gauntlet and defend their Logic against the 
attacks of European critics. Till very lately they entertained a very 
low opinion of European Logic, some account of wliich had been 
supplied to them from the popular work of Abercrombie. The 
European style is to them not sufficiently precise. The use of an 
abstract, instead of a concrete term is enough to disgust a Brahman. 
Besides, he wants to see all results put forward in short and clear 
language, and to have all possible objections carefully weighed and 
refuted. By the exertions of Dr. Ballantyne, the Principal of the 
Sanskrit College at Benares, some of the best English works on 
Logic have been made accessible to the Pandits, and at the present 
day we might hear the merits of Bacon's Novum Organon discussed 
in the streets of Benares. Indian Philosophy therefore should not 
be attacked at random. Thales or Empedocles can be criticized in 
the schools with impunity, but Kan&da and Gotama may find cham 
pions in India, if not in Europe. 



INDEXe 



INDEX. 



Abstractiok, 95, 96. 

does it imply generalization 1 

126. 
Abstract and concrete, 116. 
Accident, 140. 
All, ambiguous, 158. 
Ampliatiye judgments, 168. 
Analogy, 289. 
Analytic and dialectic, 74. 
Anticipation, 266. 
A posteriori, 66. 
A priori, 66. 
Art and science, 26. 
Art, unconsciousness in, 29. 
Attribute, 145, 
Attribute and substitute, 141. 
Axiom, 312. 

Belief, degrees of, 278. 

— — according to Aristotle, 280. 

Categories, 313. 
Categorical, 146. 
Cause and effect, 227. 
Causes, search for, 254. 
Chances, doctrine of, 293. 
Classification, 302. 
Cognitions, adequate and inade- 
quate, 91, 92. 

clear and obscure, 91. 

confused and distinct, 92. 

— — symbolical and notative, 93. 
Colligation, 269. 
Comparison, 95. 
Conceptions, 93. 

complex, inference by, 188. 

— ■ — formation of, 94. 

form and contents of, 31, 32. 

— — higher and lower, 96. 
inductive, 269. 



Conceptions, notative and iuttii- 

tive, 52. 

privative, 112. 

relative, 114. 

scheme of, as to their three 

powers, 100. 
Concrete and abstract, 116. 
Contradiction, principle of, 248. 
Contradictory opposition, 178. 
Contrary opposition, 179. 
Conversion, 182. 

simple and per accidens, 183. 

Copula, meaning of, 157. 
Corollary, 313. 
Criterion of truth, 247. 

Deduction and induction, 251. 
Definition, 107, 142, 269. 

aids division, 108. 

as a predicable, 138. 

rules of, 108. 

sources of, 143. 

table of, 145. 

and division, 310. 

Denomination, 96, 110, 222. 

in a judgment, 166. 

Determinants, inference by add- 
ing, 187. 
Determination, 102. 
Difference, 136. 
Dilemma, 236. 
Disjunctive, 146. 

judgment, inference by, 190. 

Distribution of terms, 156. 
Division, 103. 

rules of, 103. 

and definition, 310. 

aids definition, 108. 

Elenchus, 309. 



344 



INDEX. 



Enthymeme, the rhetorical, 284. 

Episyllogism, 240. 

Errors, 309. 

Example, 287. 

Excluded middle, principle of, 

249. 
Explicative judgments, 168. 
Extension, 222. 

of judgments, 195. 

and intension, 99. 

Fallacies, 309. 

Figure of syllogism, the fourth, 

206. 
Figures of syllogism, three, 201. 

their special canons, 205. 

Form, and matter, 33. 

passages to illustrate, 38. 

Form, senses of the word, 37. 

Generalization, 96. 
Genus, 97, 136, 139. 

summum, 97, 98. 

Grammar, imiversal, 58. 

Hamilton's (Sir W.) account of 

judgments, 162. 
Hypothesis, 312. 
Hypothetical, 146. 

Identity, principle of, 249. 
Immediate inference, 174. 
Inconsistent opposition, 179. 
Indian Logic, 325. 
Individual, 97. 
Induction, canon of, 273. 

complete and incomplete, 272. 

and deduction, 251. 

Inference, mediate, canon of, 192. 

mediate and immediate, 174. 

threefold import of, 222. 

Instance, 309. 
Intension, 99, 222. 

of judgments, 165. 

Intuitions, 93. 

— — and conceptions, 93, 126. 
Intentions, first and second, 40, 41. 
Interpretation, inference of, 188. 

Judgment, 133. 

Judgments, categorical, hypothet- 
ical, and disjunctive, 146. 



Judgments, explicative aul am 
pliative, 168. 

indefinite, 155. 

plurative, 154. 

quahty of, 154. 

relation of, 145. 

quantity of, 153 

tabular analysis of, 160. 

threefold import of, 165. 

Language, 42. 

analyzes thought, 44. 

Languages, analytic and synthet- 
ic, 45. 

Language divided, 43. 

functions of, 43. 

how far imitative, 63. 

of the arts, 48. 

origin of, 61. 

records thought, 49. 

abbreviates thought, 52. 

communicates thought, 54. 

what it includes, 43. 

Lemma, 313. 

Logic, an a priori science, 66. 

a science, 26. 

apphed, 245. 

defined, 20. 

how related to language, 43 

Indian, 325. 

origin of, 17. 

pure and applied, 23. 

threefold division of, 83 ; ob- 
jections to this, 84. 

twofold view of, 21. 

uses and pretensions of, 74. 

various names of, 71. 

Marks or attributes, 98. 

Matter and form, 33. 

Mediate inference, 174, 192. 

canon of, 192. 

rules of, 193. 

Method, 310. 

Mind, critical and suggestive 
powers of, 78. 

Modality, 155. 

Modes of syllogism, 209. 

according to Sir W. Hamil- 
ton, 218. 

MiiUer, Professor, on Indian liog- 
ic, 325. 



INDEX. 



345 



Names. See Nouns. 

Names, rules for forming, 304. 

Nominalism and realism, nature 
of the dispute, 120. 

moderate, 120. 

ultra, 120. 

Notation, a mode of, 211. 

Euler's, 220. 

Notes or marks, 95. 

Notions. See Cognitions. 

Nouns, proper, singular, and com- 
mon, 110. 

distributive and collective, 

110. 

substantive, attributive, and 

relative. 111. 

positive and privative, 111. 

univocal, equivocal, or anal- 
ogous, 111. 

Objective and subjective, 35. 
Opposition, 177. 
table of, 178. 

Partition, 107. 
Postulate, 312. 
Predicables, classes of, 136. 
Predicate, distribution of, 156. 
Predicates, inference by sum of, 

191. 
Premisses, order of, 199. 
Principles, sources of, 306. 
Privative conceptions, 185. 
Problem, 174, 312. 
Property, 138. 
ProsyUogism, 240. 

Quantity of judgments, 153. 

Realism, 119. • 
ultra, 119. 



Reflection, 95. 

Relation of judgments, 145. 

in judgments, 134. 

Scholion, 313. 
Science, 246. 

and art, 26. 

Sciences, classification of, 315. 
Some ambiguous, 158. 
Sorites, 234. 

its two forms, 235. 

Species, 97. 
Species irifima, 97. 
Subaltern genus, 97. 

opposition, 181. 

Subcontrary opposition, 181. 
Subjective and objective, 35. 
Substitute and attribute, 141. 
Sufficient reason, principle of, 249 
Syllogism, 173. 
Syllogisms, conditional, 224. 

defective, 283. 

disjunctive, 230. 

deductive and inductive, 281. 

equivalent, 215. 

incomplete, 239. 

three figures of, 201. 

modes of, 209. 

the unfigured, 208. 

Tautologous judgments, 169. 
Terms, 134. 
Theorem, 312. 
Thesis, 312. 

Universale, 95. 

Universals, nature of, 116, 118. 

Words, Aristotle's view of, 5G. 
Words, how far essential *a 
thought, 60, 61. 



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Universal History. By E. P. Peabodt. Arranged to 
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chai'ts with colors. As he progresses, each color will disseminate 
the .career of a nation in time as far as there is extant chronological 
data for it, and thus the history of ditFerent nations will form of one 
chart a symmetrical picture. Thus the outlines of history are pre- 
sented to the eye for future reference and additional data by the 
student, as pupils now so profitably produce geographical maps fi-om 
the detailed description of books. The result is their own work, and 
an interesting proof of their intelligence, attention, and discrimina- 
tion. 

Teachers are invited to an examination of this method of illus- 
trating the studies of their scholars in history, when it will be seen 
that the time given to this study may be made interesting and very 
profitable to themselves and the pupils under their charge. 

Fitch's Mapping' Plates ; designed for Learners in Ge- 
ography, being a collection of Plates prepared for Delineating 
Maps of the World, and Countries forming its principal subdivi- 
sions, viz., 1. The World. 2. United States. 3. North America. 
4. South America. 5. A State. 6. Mexico and Guatemala. 
7. Great Britain and Ireland, 8. Europe. 9. Southern Europe. 
10. Germany. 11. Africa. 12. Asia. 13. Atlantic Ocean. 14. Pa- 
cific Ocean. By Geokgb W. Fitch. Price 30 cents. 

• The. attention of the public is respectfully called to the above 
plates, and to the advantages they are calculated to afford in the 
study of Geography. They are prepared with the suitable and 
requisite lines of latitude and longitude, for maps of the world, and 
the countries forming its principal subdivisions, and are designed to 
be used in connection with the school atlases in common use, as well 
as with outline maps. With these Plates, the pupil is able to com- 
mence, at once, the delineation of maps, without the difficult and 
perplexing labor of drawing the meridians and parallels — a labor 
•which generally consumes the time of both teacher and scholar, to 
an extent entirely disproportionate to any good which may be de- 
rived thereby. 



12 SCHOOL AND COLLEGE TEXT-BOOKS. 

Hazen's Speller and ©efiner. The Speller and Definer, 

or Class-Book No. 2, designed to answer the purposes of a spelling- 
book, and to supersede the necessity of the use of a dictionary as a 
class-book. By E. Hazen, A. M. Price 20 cents. 

Ct^ Over 500,000 volumes of this book have been sold. 

This Speller and Definer was first published in 1829, and has stood 
the test of the school-room successfully to the present day. It was 
thoroughly revised by the author in 1857, and is now called superior 
to any other book of the kind in use. 'At the time it was first pub- 
lished, it was the practice in nearly all the schools to try to commit 
to memory Walker's School Dictionary, but through the influence 
of this book dictionaries in this application were nearly banished in 
a few years. 

Hazen's Syml)«Iic Spelling* Book. With 553 Cuts. 

Price 20 cents. 
Hazen's Symbolic Spelling Book. Part 1st, 288 Cuts. Price 

10 cents. 
Hazen's Symbolic Spelling Book. Part 2d, 265 Cuts. Price 

12 cents. 

The Symbolic Speller is intended to precede Hazen's Speller and 
Definer. From the reading lessons of this spelling book, pupils may 
leai-n the meaning and application of a great number of words- which 
will serve as a good foundation for the explanation of others. 

Miles's United States Speller. A new work, containing 

upwards of fifteen thousand of the most common English words. 
Price 13 cents. 

The author of this work is an old Practical Teacher. The ar- 
rangements and classification are original and strictly progressive ; 
and in Orthography and Pronunciation, the best standard authors, 
writers, and speakers, have been consulted. 

These Spelling-Books are designed to accompany Webb's Series 
of Normal Readers. 

Kirkliara'S Elocution. 12mo. 357 pages. Price 75 
cents. 

This is one of the best Elocutions ever printed. It contains a 
varied and interesting selection of very useful matter, carefully 
arranged. It is a standard work, and now used in some of the best 
schools in the country ; among which are the Normal School, Phil- 
adelphia ; Lower Canada College ; Toronto Academy, etc. 



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